https://katlas.org/index.php?action=history&feed=atom&title=Data%3ABraiding%2FA_1%2F1%2F6 2026-10-31T05:35:43Z Revision history for this page on the wiki MediaWiki 1.39.6 https://katlas.org/index.php?title=Data:Braiding/A_1/1/6&diff=582538&oldid=prev 2006-06-22T02:37:08Z

<p></p> <table style="background-color: #fff; color: #202122;" data-mw="interface"> <col class="diff-marker" /> <col class="diff-content" /> <col class="diff-marker" /> <col class="diff-content" /> <tr class="diff-title" lang="en"> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← Older revision</td> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 22:37, 21 June 2006</td> </tr><tr> <td colspan="2" class="diff-lineno">Line 1:</td> <td colspan="2" class="diff-lineno">Line 1:</td> </tr> <tr> <td class="diff-marker" data-marker="−"></td> <td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del style="font-weight: bold; text-decoration: none;">{{1, {{{{q^(-1), 0, -q^(-5), 0, -q^(-4)}, {0, q^(-1), -q^(-4), 0, 0}, {0, 0, -q^(-3), 0, 0}, {0, 0, 0, q^(-1), -q^(-4)}, {0, 0, 0, 0, -q^(-3)}}, {{q^(-1), 0, 0, 0, 0}, {0, 0, q^(-2), 0, 0}, {0, q^(-2), -((1 - q^2)/q^3), 0, 0}, {0, 0, 0, 0, q^(-2)}, {0, 0, 0, q^(-2), -((1 - q^2)/q^3)}}, {{0, q^(-2), 0, 0, -q^(-6)}, {q^(-2), -((1 - q^2)/q^3), 0, 0, -q^(-5)}, {0, 0, q^(-1), 0, -q^(-4)}, {0, 0, 0, q^(-1), -q^(-4)}, {0, 0, 0, 0, -q^(-3)}}, {{q^(-1), 0, 0, 0, 0}, {0, 0, 0, q^(-2), 0}, {0, 0, 0, 0, q^(-2)}, {0, q^(-2), 0, -((1 - q^2)/q^3), 0}, {0, 0, q^(-2), 0, -((1 - q^2)/q^3)}}, {{q^(-1), 0, 0, -q^(-5), -q^(-4)}, {0, q^(-1), 0, -q^(-4), 0}, {0, 0, q^(-1), 0, -q^(-4)}, {0, 0, 0, -q^(-3), 0}, {0, 0, 0, 0, -q^(-3)}}}, {{{q, 0, -q^(-1), 0, -1}, {0, q, -1, 0, 0}, {0, 0, -q^3, 0, 0}, {0, 0, 0, q, -1}, {0, 0, 0, 0, -q^3}}, {{q, 0, 0, 0, 0}, {0, q - q^3, q^2, 0, 0}, {0, q^2, 0, 0, 0}, {0, 0, 0, q - q^3, q^2}, {0, 0, 0, q^2, 0}}, {{q - q^3, q^2, 0, 0, -q^(-2)}, {q^2, 0, 0, 0, -q^(-1)}, {0, 0, q, 0, -1}, {0, 0, 0, q, -1}, {0, 0, 0, 0, -q^3}}, {{q, 0, 0, 0, 0}, {0, q - q^3, 0, q^2, 0}, {0, 0, q - q^3, 0, q^2}, {0, q^2, 0, 0, 0}, {0, 0, q^2, 0, 0}}, {{q, 0, 0, -q^(-1), -1}, {0, q, 0, -1, 0}, {0, 0, q, 0, -1}, {0, 0, 0, -q^3, 0}, {0, 0, 0, 0, -q^3}}}}}, {1 + q^(-2) + q^2, {{{{q^(-1), 0, 0, -q^(-6), 0, 0, -q^(-5), 0, 0}, {0, q^(-1), 0, -q^(-5), 0, 0, 0, 0, -q^(-5)}, {0, 0, q^(-1), -q^(-4), 0, 0, 0, 0, 0}, {0, 0, 0, -q^(-3), 0, 0, 0, 0, 0}, {0, 0, 0, 0, q^(-1), 0, -q^(-5), 0, -q^(-4)}, {0, 0, 0, 0, 0, q^(-1), -q^(-4), 0, 0}, {0, 0, 0, 0, 0, 0, -q^(-3), 0, 0}, {0, 0, 0, 0, 0, 0, 0, q^(-1), -q^(-4)}, {0, 0, 0, 0, 0, 0, 0, 0, -q^(-3)}}, {{q^(-1), 0, 0, 0, 0, 0, 0, 0, 0}, {0, q^(-1), 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, q^(-2), 0, 0, 0, 0, 0}, {0, 0, q^(-2), -((1 - q^2)/q^3), 0, 0, 0, 0, 0}, {0, 0, 0, 0, q^(-1), 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, q^(-2), 0, 0}, {0, 0, 0, 0, 0, q^(-2), -((1 - q^2)/q^3), 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, q^(-2)}, {0, 0, 0, 0, 0, 0, 0, q^(-2), -((1 - q^2)/q^3)}}, {{q^(-1), 0, 0, 0, 0, 0, 0, 0, -q^(-8)}, {0, 0, q^(-2), 0, 0, 0, 0, 0, -q^(-7)}, {0, q^(-2), -((1 - q^2)/q^3), 0, 0, 0, 0, 0, -q^(-6)}, {0, 0, 0, q^(-1), 0, 0, 0, 0, -q^(-5)}, {0, 0, 0, 0, 0, q^(-2), 0, 0, -q^(-6)}, {0, 0, 0, 0, q^(-2), -((1 - q^2)/q^3), 0, 0, -q^(-5)}, {0, 0, 0, 0, 0, 0, q^(-1), 0, -q^(-4)}, {0, 0, 0, 0, 0, 0, 0, q^(-1), -q^(-4)}, {0, 0, 0, 0, 0, 0, 0, 0, -q^(-3)}}, {{0, q^(-2), 0, 0, 0, 0, 0, 0, 0}, {q^(-2), -((1 - q^2)/q^3), 0, 0, 0, 0, 0, 0, 0}, {0, 0, q^(-1), 0, 0, 0, 0, 0, 0}, {0, 0, 0, q^(-1), 0, 0, 0, 0, 0}, {0, 0, 0, 0, q^(-1), 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, q^(-2), 0}, {0, 0, 0, 0, 0, 0, 0, 0, q^(-2)}, {0, 0, 0, 0, 0, q^(-2), 0, -((1 - q^2)/q^3), 0}, {0, 0, 0, 0, 0, 0, q^(-2), 0, -((1 - q^2)/q^3)}}, {{q^(-1), 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, q^(-2), 0, 0, 0, 0}, {0, 0, 0, 0, 0, q^(-2), 0, 0, 0}, {0, 0, 0, 0, 0, 0, q^(-2), 0, 0}, {0, q^(-2), 0, 0, -((1 - q^2)/q^3), 0, 0, 0, 0}, {0, 0, q^(-2), 0, 0, -((1 - q^2)/q^3), 0, 0, 0}, {0, 0, 0, q^(-2), 0, 0, -((1 - q^2)/q^3), 0, 0}, {0, 0, 0, 0, 0, 0, 0, q^(-1), 0}, {0, 0, 0, 0, 0, 0, 0, 0, q^(-1)}}}, {{{q, 0, 0, -q^(-2), 0, 0, -q^(-1), 0, 0}, {0, q, 0, -q^(-1), 0, 0, 0, 0, -q^(-1)}, {0, 0, q, -1, 0, 0, 0, 0, 0}, {0, 0, 0, -q^3, 0, 0, 0, 0, 0}, {0, 0, 0, 0, q, 0, -q^(-1), 0, -1}, {0, 0, 0, 0, 0, q, -1, 0, 0}, {0, 0, 0, 0, 0, 0, -q^3, 0, 0}, {0, 0, 0, 0, 0, 0, 0, q, -1}, {0, 0, 0, 0, 0, 0, 0, 0, -q^3}}, {{q, 0, 0, 0, 0, 0, 0, 0, 0}, {0, q, 0, 0, 0, 0, 0, 0, 0}, {0, 0, q - q^3, q^2, 0, 0, 0, 0, 0}, {0, 0, q^2, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, q, 0, 0, 0, 0}, {0, 0, 0, 0, 0, q - q^3, q^2, 0, 0}, {0, 0, 0, 0, 0, q^2, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, q - q^3, q^2}, {0, 0, 0, 0, 0, 0, 0, q^2, 0}}, {{q, 0, 0, 0, 0, 0, 0, 0, -q^(-4)}, {0, q - q^3, q^2, 0, 0, 0, 0, 0, -q^(-3)}, {0, q^2, 0, 0, 0, 0, 0, 0, -q^(-2)}, {0, 0, 0, q, 0, 0, 0, 0, -q^(-1)}, {0, 0, 0, 0, q - q^3, q^2, 0, 0, -q^(-2)}, {0, 0, 0, 0, q^2, 0, 0, 0, -q^(-1)}, {0, 0, 0, 0, 0, 0, q, 0, -1}, {0, 0, 0, 0, 0, 0, 0, q, -1}, {0, 0, 0, 0, 0, 0, 0, 0, -q^3}}, {{q - q^3, q^2, 0, 0, 0, 0, 0, 0, 0}, {q^2, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, q, 0, 0, 0, 0, 0, 0}, {0, 0, 0, q, 0, 0, 0, 0, 0}, {0, 0, 0, 0, q, 0, 0, 0, 0}, {0, 0, 0, 0, 0, q - q^3, 0, q^2, 0}, {0, 0, 0, 0, 0, 0, q - q^3, 0, q^2}, {0, 0, 0, 0, 0, q^2, 0, 0, 0}, {0, 0, 0, 0, 0, 0, q^2, 0, 0}}, {{q, 0, 0, 0, 0, 0, 0, 0, 0}, {0, q - q^3, 0, 0, q^2, 0, 0, 0, 0}, {0, 0, q - q^3, 0, 0, q^2, 0, 0, 0}, {0, 0, 0, q - q^3, 0, 0, q^2, 0, 0}, {0, q^2, 0, 0, 0, 0, 0, 0, 0}, {0, 0, q^2, 0, 0, 0, 0, 0, 0}, {0, 0, 0, q^2, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, q, 0}, {0, 0, 0, 0, 0, 0, 0, 0, q}}}}}, {1 + q^(-4) + q^(-2) + q^2 + q^4, {{{{q^(-1), 0, 0, 0, -q^(-7)}, {0, q^(-1), 0, 0, -q^(-6)}, {0, 0, q^(-1), 0, -q^(-5)}, {0, 0, 0, q^(-1), -q^(-4)}, {0, 0, 0, 0, -q^(-3)}}, {{q^(-1), 0, 0, 0, 0}, {0, q^(-1), 0, 0, 0}, {0, 0, q^(-1), 0, 0}, {0, 0, 0, 0, q^(-2)}, {0, 0, 0, q^(-2), -((1 - q^2)/q^3)}}, {{q^(-1), 0, 0, 0, 0}, {0, q^(-1), 0, 0, 0}, {0, 0, 0, q^(-2), 0}, {0, 0, q^(-2), -((1 - q^2)/q^3), 0}, {0, 0, 0, 0, q^(-1)}}, {{q^(-1), 0, 0, 0, 0}, {0, 0, q^(-2), 0, 0}, {0, q^(-2), -((1 - q^2)/q^3), 0, 0}, {0, 0, 0, q^(-1), 0}, {0, 0, 0, 0, q^(-1)}}, {{0, q^(-2), 0, 0, 0}, {q^(-2), -((1 - q^2)/q^3), 0, 0, 0}, {0, 0, q^(-1), 0, 0}, {0, 0, 0, q^(-1), 0}, {0, 0, 0, 0, q^(-1)}}}, {{{q, 0, 0, 0, -q^(-3)}, {0, q, 0, 0, -q^(-2)}, {0, 0, q, 0, -q^(-1)}, {0, 0, 0, q, -1}, {0, 0, 0, 0, -q^3}}, {{q, 0, 0, 0, 0}, {0, q, 0, 0, 0}, {0, 0, q, 0, 0}, {0, 0, 0, q - q^3, q^2}, {0, 0, 0, q^2, 0}}, {{q, 0, 0, 0, 0}, {0, q, 0, 0, 0}, {0, 0, q - q^3, q^2, 0}, {0, 0, q^2, 0, 0}, {0, 0, 0, 0, q}}, {{q, 0, 0, 0, 0}, {0, q - q^3, q^2, 0, 0}, {0, q^2, 0, 0, 0}, {0, 0, 0, q, 0}, {0, 0, 0, 0, q}}, {{q - q^3, q^2, 0, 0, 0}, {q^2, 0, 0, 0, 0}, {0, 0, q, 0, 0}, {0, 0, 0, q, 0}, {0, 0, 0, 0, q}}}}}, {1 + q^(-6) + q^(-4) + q^(-2) + q^2 + q^4 + q^6, {{{{q^(-1)}}, {{q^(-1)}}, {{q^(-1)}}, {{q^(-1)}}, {{q^(-1)}}}, {{{q}}, {{q}}, {{q}}, {{q}}, {{q}}}}}}</del></div></td> <td class="diff-marker" data-marker="+"></td> <td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">{{1 + q^(-6) + q^(-4) + q^(-2) + q^2 + q^4 + q^6, {{{{q^(-1)}}, {{q^(-1)}}, {{q^(-1)}}, {{q^(-1)}}, {{q^(-1)}}}, {{{q}}, {{q}}, {{q}}, {{q}}, {{q}}}}}, {1 + q^(-4) + q^(-2) + q^2 + q^4, {{{{q^(-1), 0, 0, 0, 0}, {0, q^(-1), 0, 0, 0}, {0, 0, q^(-1), 0, 0}, {0, 0, 0, q^(-1), 0}, {0, 0, 0, 0, -q^(-3)}}, {{q^(-1), 0, 0, 0, 0}, {0, q^(-1), 0, 0, 0}, {0, 0, q^(-1), 0, 0}, {0, 0, 0, -(1/(q^3*(1 + q^2))), (1 + q^2 + q^4)/(q^2*(1 + q^2)^2)}, {0, 0, 0, q^(-2), q/(1 + q^2)}}, {{q^(-1), 0, 0, 0, 0}, {0, q^(-1), 0, 0, 0}, {0, 0, -(1/(q^3*(1 + q^2 + q^4))), (1 + 2*q^2 + 2*q^4 + 2*q^6 + q^8)/(q^2*(1 + q^2 + q^4)^2), 0}, {0, 0, q^(-2), q^3/(1 + q^2 + q^4), 0}, {0, 0, 0, 0, q^(-1)}}, {{q^(-1), 0, 0, 0, 0}, {0, -(1/(q^3*(1 + q^2 + q^4 + q^6))), (1 + 2*q^2 + 3*q^4 + 3*q^6 + 3*q^8 + 2*q^10 + q^12)/(q^2*(1 + q^2 + q^4 + q^6)^2), 0, 0}, {0, q^(-2), q^5/(1 + q^2 + q^4 + q^6), 0, 0}, {0, 0, 0, q^(-1), 0}, {0, 0, 0, 0, q^(-1)}}, {{-(1/(q^3*(1 + q^2 + q^4 + q^6 + q^8))), (1 + 2*q^2 + 3*q^4 + 4*q^6 + 4*q^8 + 4*q^10 + 3*q^12 + 2*q^14 + q^16)/(q^2*(1 + q^2 + q^4 + q^6 + q^8)^2), 0, 0, 0}, {q^(-2), q^7/(1 + q^2 + q^4 + q^6 + q^8), 0, 0, 0}, {0, 0, q^(-1), 0, 0}, {0, 0, 0, q^(-1), 0}, {0, 0, 0, 0, q^(-1)}}}, {{{q, 0, 0, 0, 0}, {0, q, 0, 0, 0}, {0, 0, q, 0, 0}, {0, 0, 0, q, 0}, {0, 0, 0, 0, -q^3}}, {{q, 0, 0, 0, 0}, {0, q, 0, 0, 0}, {0, 0, q, 0, 0}, {0, 0, 0, -(q^5/(1 + q^2)), (q^2*(1 + q^2 + q^4))/(1 + q^2)^2}, {0, 0, 0, q^2, q/(1 + q^2)}}, {{q, 0, 0, 0, 0}, {0, q, 0, 0, 0}, {0, 0, -(q^7/(1 + q^2 + q^4)), (q^2*(1 + 2*q^2 + 2*q^4 + 2*q^6 + q^8))/(1 + q^2 + q^4)^2, 0}, {0, 0, q^2, q/(1 + q^2 + q^4), 0}, {0, 0, 0, 0, q}}, {{q, 0, 0, 0, 0}, {0, -(q^9/(1 + q^2 + q^4 + q^6)), (q^2*(1 + 2*q^2 + 3*q^4 + 3*q^6 + 3*q^8 + 2*q^10 + q^12))/(1 + q^2 + q^4 + q^6)^2, 0, 0}, {0, q^2, q/(1 + q^2 + q^4 + q^6), 0, 0}, {0, 0, 0, q, 0}, {0, 0, 0, 0, q}}, {{-(q^11/(1 + q^2 + q^4 + q^6 + q^8)), (q^2*(1 + 2*q^2 + 3*q^4 + 4*q^6 + 4*q^8 + 4*q^10 + 3*q^12 + 2*q^14 + q^16))/(1 + q^2 + q^4 + q^6 + q^8)^2, 0, 0, 0}, {q^2, q/(1 + q^2 + q^4 + q^6 + q^8), 0, 0, 0}, {0, 0, q, 0, 0}, {0, 0, 0, q, 0}, {0, 0, 0, 0, q}}}}}, {1 + q^(-2) + q^2, {{{{q^(-1), 0, 0, 0, 0, 0, 0, 0, 0}, {0, q^(-1), 0, 0, 0, 0, 0, 0, 0}, {0, 0, q^(-1), 0, 0, 0, 0, 0, 0}, {0, 0, 0, -q^(-3), 0, 0, 0, 0, 0}, {0, 0, 0, 0, q^(-1), 0, 0, 0, 0}, {0, 0, 0, 0, 0, q^(-1), 0, 0, 0}, {0, 0, 0, 0, 0, 0, -q^(-3), 0, 0}, {0, 0, 0, 0, 0, 0, 0, q^(-1), 0}, {0, 0, 0, 0, 0, 0, 0, 0, -q^(-3)}}, {{q^(-1), 0, 0, 0, 0, 0, 0, 0, 0}, {0, q^(-1), 0, 0, 0, 0, 0, 0, 0}, {0, 0, -(1/(q^3*(1 + q^2))), (1 + q^2 + q^4)/(q^2*(1 + q^2)^2), 0, 0, 0, 0, 0}, {0, 0, q^(-2), q/(1 + q^2), 0, 0, 0, 0, 0}, {0, 0, 0, 0, q^(-1), 0, 0, 0, 0}, {0, 0, 0, 0, 0, -(1/(q^3*(1 + q^2))), (1 + q^2 + q^4)/(q^2*(1 + q^2)^2), 0, 0}, {0, 0, 0, 0, 0, q^(-2), q/(1 + q^2), 0, 0}, {0, 0, 0, 0, 0, 0, 0, -(1/(q^3*(1 + q^2))), (1 + q^2 + q^4)/(q^2*(1 + q^2)^2)}, {0, 0, 0, 0, 0, 0, 0, q^(-2), q/(1 + q^2)}}, {{q^(-1), 0, 0, 0, 0, 0, 0, 0, 0}, {0, -(1/(q^3*(1 + q^2 + q^4))), (1 + 2*q^2 + 2*q^4 + 2*q^6 + q^8)/(q^2*(1 + q^2 + q^4)^2), 0, 0, 0, 0, 0, 0}, {0, q^(-2), q^3/(1 + q^2 + q^4), 0, 0, 0, 0, 0, 0}, {0, 0, 0, q^(-1), 0, 0, 0, 0, 0}, {0, 0, 0, 0, -(1/(q^3*(1 + q^2 + q^4))), (1 + 2*q^2 + 2*q^4 + 2*q^6 + q^8)/(q^2*(1 + q^2 + q^4)^2), 0, 0, 0}, {0, 0, 0, 0, q^(-2), q^3/(1 + q^2 + q^4), 0, 0, 0}, {0, 0, 0, 0, 0, 0, q^(-1), 0, 0}, {0, 0, 0, 0, 0, 0, 0, q^(-1), 0}, {0, 0, 0, 0, 0, 0, 0, 0, -q^(-3)}}, {{-(1/(q^3*(1 + q^2 + q^4 + q^6))), (1 + 2*q^2 + 3*q^4 + 3*q^6 + 3*q^8 + 2*q^10 + q^12)/(q^2*(1 + q^2 + q^4 + q^6)^2), 0, 0, 0, 0, 0, 0, 0}, {q^(-2), q^5/(1 + q^2 + q^4 + q^6), 0, 0, 0, 0, 0, 0, 0}, {0, 0, q^(-1), 0, 0, 0, 0, 0, 0}, {0, 0, 0, q^(-1), 0, 0, 0, 0, 0}, {0, 0, 0, 0, q^(-1), 0, 0, 0, 0}, {0, 0, 0, 0, 0, -(1/(q^3*(1 + q^2))), 0, (1 + q^2 + q^4)/(q^2*(1 + q^2)^2), 0}, {0, 0, 0, 0, 0, 0, -(1/(q^3*(1 + q^2))), 0, (1 + q^2 + q^4)/(q^2*(1 + q^2)^2)}, {0, 0, 0, 0, 0, q^(-2), 0, q/(1 + q^2), 0}, {0, 0, 0, 0, 0, 0, q^(-2), 0, q/(1 + q^2)}}, {{q^(-1), 0, 0, 0, 0, 0, 0, 0, 0}, {0, -(1/(q^3*(1 + q^2 + q^4))), 0, 0, (1 + 2*q^2 + 2*q^4 + 2*q^6 + q^8)/(q^2*(1 + q^2 + q^4)^2), 0, 0, 0, 0}, {0, 0, -(1/(q^3*(1 + q^2 + q^4))), 0, 0, (1 + 2*q^2 + 2*q^4 + 2*q^6 + q^8)/(q^2*(1 + q^2 + q^4)^2), 0, 0, 0}, {0, 0, 0, -(1/(q^3*(1 + q^2 + q^4))), 0, 0, (1 + 2*q^2 + 2*q^4 + 2*q^6 + q^8)/(q^2*(1 + q^2 + q^4)^2), 0, 0}, {0, q^(-2), 0, 0, q^3/(1 + q^2 + q^4), 0, 0, 0, 0}, {0, 0, q^(-2), 0, 0, q^3/(1 + q^2 + q^4), 0, 0, 0}, {0, 0, 0, q^(-2), 0, 0, q^3/(1 + q^2 + q^4), 0, 0}, {0, 0, 0, 0, 0, 0, 0, q^(-1), 0}, {0, 0, 0, 0, 0, 0, 0, 0, q^(-1)}}}, {{{q, 0, 0, 0, 0, 0, 0, 0, 0}, {0, q, 0, 0, 0, 0, 0, 0, 0}, {0, 0, q, 0, 0, 0, 0, 0, 0}, {0, 0, 0, -q^3, 0, 0, 0, 0, 0}, {0, 0, 0, 0, q, 0, 0, 0, 0}, {0, 0, 0, 0, 0, q, 0, 0, 0}, {0, 0, 0, 0, 0, 0, -q^3, 0, 0}, {0, 0, 0, 0, 0, 0, 0, q, 0}, {0, 0, 0, 0, 0, 0, 0, 0, -q^3}}, {{q, 0, 0, 0, 0, 0, 0, 0, 0}, {0, q, 0, 0, 0, 0, 0, 0, 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0, 0, 0, 0, 0}, {0, 0, 0, q, 0, 0, 0, 0, 0}, {0, 0, 0, 0, q, 0, 0, 0, 0}, {0, 0, 0, 0, 0, -(q^5/(1 + q^2)), 0, (q^2 + q^4 + q^6)/(1 + q^2)^2, 0}, {0, 0, 0, 0, 0, 0, -(q^5/(1 + q^2)), 0, (q^2 + q^4 + q^6)/(1 + q^2)^2}, {0, 0, 0, 0, 0, q^2, 0, q/(1 + q^2), 0}, {0, 0, 0, 0, 0, 0, q^2, 0, q/(1 + q^2)}}, {{q, 0, 0, 0, 0, 0, 0, 0, 0}, {0, -(q^7/(1 + q^2 + q^4)), 0, 0, ((q + q^3)^2*(1 + q^4))/(1 + q^2 + q^4)^2, 0, 0, 0, 0}, {0, 0, -(q^7/(1 + q^2 + q^4)), 0, 0, ((q + q^3)^2*(1 + q^4))/(1 + q^2 + q^4)^2, 0, 0, 0}, {0, 0, 0, -(q^7/(1 + q^2 + q^4)), 0, 0, ((q + q^3)^2*(1 + q^4))/(1 + q^2 + q^4)^2, 0, 0}, {0, q^2, 0, 0, q/(1 + q^2 + q^4), 0, 0, 0, 0}, {0, 0, q^2, 0, 0, q/(1 + q^2 + q^4), 0, 0, 0}, {0, 0, 0, q^2, 0, 0, q/(1 + q^2 + q^4), 0, 0}, {0, 0, 0, 0, 0, 0, 0, q, 0}, {0, 0, 0, 0, 0, 0, 0, 0, q}}}}}, {1, {{{{q^(-1), 0, 0, 0, 0}, {0, q^(-1), 0, 0, 0}, {0, 0, -q^(-3), 0, 0}, {0, 0, 0, q^(-1), 0}, {0, 0, 0, 0, -q^(-3)}}, {{q^(-1), 0, 0, 0, 0}, {0, -(1/(q^3*(1 + q^2))), (1 + q^2 + q^4)/(q^2*(1 + q^2)^2), 0, 0}, {0, q^(-2), q/(1 + q^2), 0, 0}, {0, 0, 0, -(1/(q^3*(1 + q^2))), (1 + q^2 + q^4)/(q^2*(1 + q^2)^2)}, {0, 0, 0, q^(-2), q/(1 + q^2)}}, {{-(1/(q^3*(1 + q^2 + q^4))), (1 + 2*q^2 + 2*q^4 + 2*q^6 + q^8)/(q^2*(1 + q^2 + q^4)^2), 0, 0, 0}, {q^(-2), q^3/(1 + q^2 + q^4), 0, 0, 0}, {0, 0, q^(-1), 0, 0}, {0, 0, 0, q^(-1), 0}, {0, 0, 0, 0, -q^(-3)}}, {{q^(-1), 0, 0, 0, 0}, {0, -(1/(q^3*(1 + q^2))), 0, (1 + q^2 + q^4)/(q^2*(1 + q^2)^2), 0}, {0, 0, -(1/(q^3*(1 + q^2))), 0, (1 + q^2 + q^4)/(q^2*(1 + q^2)^2)}, {0, q^(-2), 0, q/(1 + q^2), 0}, {0, 0, q^(-2), 0, q/(1 + q^2)}}, {{q^(-1), 0, 0, 0, 0}, {0, q^(-1), 0, 0, 0}, {0, 0, q^(-1), 0, 0}, {0, 0, 0, -q^(-3), 0}, {0, 0, 0, 0, -q^(-3)}}}, {{{q, 0, 0, 0, 0}, {0, q, 0, 0, 0}, {0, 0, -q^3, 0, 0}, {0, 0, 0, q, 0}, {0, 0, 0, 0, -q^3}}, {{q, 0, 0, 0, 0}, {0, -(q^5/(1 + q^2)), (q^2*(1 + q^2 + q^4))/(1 + q^2)^2, 0, 0}, {0, q^2, q/(1 + q^2), 0, 0}, {0, 0, 0, -(q^5/(1 + q^2)), (q^2*(1 + q^2 + q^4))/(1 + q^2)^2}, {0, 0, 0, q^2, q/(1 + q^2)}}, {{-(q^7/(1 + q^2 + q^4)), (q^2*(1 + 2*q^2 + 2*q^4 + 2*q^6 + q^8))/(1 + q^2 + q^4)^2, 0, 0, 0}, {q^2, q/(1 + q^2 + q^4), 0, 0, 0}, {0, 0, q, 0, 0}, {0, 0, 0, q, 0}, {0, 0, 0, 0, -q^3}}, {{q, 0, 0, 0, 0}, {0, -(q^5/(1 + q^2)), 0, (q^2*(1 + q^2 + q^4))/(1 + q^2)^2, 0}, {0, 0, -(q^5/(1 + q^2)), 0, (q^2*(1 + q^2 + q^4))/(1 + q^2)^2}, {0, q^2, 0, q/(1 + q^2), 0}, {0, 0, q^2, 0, q/(1 + q^2)}}, {{q, 0, 0, 0, 0}, {0, q, 0, 0, 0}, {0, 0, q, 0, 0}, {0, 0, 0, -q^3, 0}, {0, 0, 0, 0, -q^3}}}}}}</ins></div></td> </tr> </table>

ScottDataRobot https://katlas.org/index.php?title=Data:Braiding/A_1/1/6&diff=49994&oldid=prev 2006-06-06T20:53:21Z

<p></p> <p><b>New page</b></p><div>{{1, {{{{q^(-1), 0, -q^(-5), 0, -q^(-4)}, {0, q^(-1), -q^(-4), 0, 0}, {0, 0, -q^(-3), 0, 0}, {0, 0, 0, q^(-1), -q^(-4)}, {0, 0, 0, 0, -q^(-3)}}, {{q^(-1), 0, 0, 0, 0}, {0, 0, q^(-2), 0, 0}, {0, q^(-2), -((1 - q^2)/q^3), 0, 0}, {0, 0, 0, 0, q^(-2)}, {0, 0, 0, q^(-2), -((1 - q^2)/q^3)}}, {{0, q^(-2), 0, 0, -q^(-6)}, {q^(-2), -((1 - q^2)/q^3), 0, 0, -q^(-5)}, {0, 0, q^(-1), 0, -q^(-4)}, {0, 0, 0, q^(-1), -q^(-4)}, {0, 0, 0, 0, -q^(-3)}}, {{q^(-1), 0, 0, 0, 0}, {0, 0, 0, q^(-2), 0}, {0, 0, 0, 0, q^(-2)}, {0, q^(-2), 0, -((1 - q^2)/q^3), 0}, {0, 0, q^(-2), 0, -((1 - q^2)/q^3)}}, {{q^(-1), 0, 0, -q^(-5), -q^(-4)}, {0, q^(-1), 0, -q^(-4), 0}, {0, 0, q^(-1), 0, -q^(-4)}, {0, 0, 0, -q^(-3), 0}, {0, 0, 0, 0, -q^(-3)}}}, {{{q, 0, -q^(-1), 0, -1}, {0, q, -1, 0, 0}, {0, 0, -q^3, 0, 0}, {0, 0, 0, q, -1}, {0, 0, 0, 0, -q^3}}, {{q, 0, 0, 0, 0}, {0, q - q^3, q^2, 0, 0}, {0, q^2, 0, 0, 0}, {0, 0, 0, q - q^3, q^2}, {0, 0, 0, q^2, 0}}, {{q - q^3, q^2, 0, 0, -q^(-2)}, {q^2, 0, 0, 0, -q^(-1)}, {0, 0, q, 0, -1}, {0, 0, 0, q, -1}, {0, 0, 0, 0, -q^3}}, {{q, 0, 0, 0, 0}, {0, q - q^3, 0, q^2, 0}, {0, 0, q - q^3, 0, q^2}, {0, q^2, 0, 0, 0}, {0, 0, q^2, 0, 0}}, {{q, 0, 0, -q^(-1), -1}, {0, q, 0, -1, 0}, {0, 0, q, 0, -1}, {0, 0, 0, -q^3, 0}, {0, 0, 0, 0, -q^3}}}}}, {1 + q^(-2) + q^2, {{{{q^(-1), 0, 0, -q^(-6), 0, 0, -q^(-5), 0, 0}, {0, q^(-1), 0, -q^(-5), 0, 0, 0, 0, -q^(-5)}, {0, 0, q^(-1), -q^(-4), 0, 0, 0, 0, 0}, {0, 0, 0, -q^(-3), 0, 0, 0, 0, 0}, {0, 0, 0, 0, q^(-1), 0, -q^(-5), 0, -q^(-4)}, {0, 0, 0, 0, 0, q^(-1), -q^(-4), 0, 0}, {0, 0, 0, 0, 0, 0, -q^(-3), 0, 0}, {0, 0, 0, 0, 0, 0, 0, q^(-1), -q^(-4)}, {0, 0, 0, 0, 0, 0, 0, 0, -q^(-3)}}, {{q^(-1), 0, 0, 0, 0, 0, 0, 0, 0}, {0, q^(-1), 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, q^(-2), 0, 0, 0, 0, 0}, {0, 0, q^(-2), -((1 - q^2)/q^3), 0, 0, 0, 0, 0}, {0, 0, 0, 0, q^(-1), 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, q^(-2), 0, 0}, {0, 0, 0, 0, 0, q^(-2), -((1 - q^2)/q^3), 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, q^(-2)}, {0, 0, 0, 0, 0, 0, 0, q^(-2), -((1 - q^2)/q^3)}}, {{q^(-1), 0, 0, 0, 0, 0, 0, 0, -q^(-8)}, {0, 0, q^(-2), 0, 0, 0, 0, 0, -q^(-7)}, {0, q^(-2), -((1 - q^2)/q^3), 0, 0, 0, 0, 0, -q^(-6)}, {0, 0, 0, q^(-1), 0, 0, 0, 0, -q^(-5)}, {0, 0, 0, 0, 0, q^(-2), 0, 0, -q^(-6)}, {0, 0, 0, 0, q^(-2), -((1 - q^2)/q^3), 0, 0, -q^(-5)}, {0, 0, 0, 0, 0, 0, q^(-1), 0, -q^(-4)}, {0, 0, 0, 0, 0, 0, 0, q^(-1), -q^(-4)}, {0, 0, 0, 0, 0, 0, 0, 0, -q^(-3)}}, {{0, q^(-2), 0, 0, 0, 0, 0, 0, 0}, {q^(-2), -((1 - q^2)/q^3), 0, 0, 0, 0, 0, 0, 0}, {0, 0, q^(-1), 0, 0, 0, 0, 0, 0}, {0, 0, 0, q^(-1), 0, 0, 0, 0, 0}, {0, 0, 0, 0, q^(-1), 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, q^(-2), 0}, {0, 0, 0, 0, 0, 0, 0, 0, q^(-2)}, {0, 0, 0, 0, 0, q^(-2), 0, -((1 - q^2)/q^3), 0}, {0, 0, 0, 0, 0, 0, q^(-2), 0, -((1 - q^2)/q^3)}}, {{q^(-1), 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, q^(-2), 0, 0, 0, 0}, {0, 0, 0, 0, 0, q^(-2), 0, 0, 0}, {0, 0, 0, 0, 0, 0, q^(-2), 0, 0}, {0, q^(-2), 0, 0, -((1 - q^2)/q^3), 0, 0, 0, 0}, {0, 0, q^(-2), 0, 0, -((1 - q^2)/q^3), 0, 0, 0}, {0, 0, 0, q^(-2), 0, 0, -((1 - q^2)/q^3), 0, 0}, {0, 0, 0, 0, 0, 0, 0, q^(-1), 0}, {0, 0, 0, 0, 0, 0, 0, 0, q^(-1)}}}, {{{q, 0, 0, -q^(-2), 0, 0, -q^(-1), 0, 0}, {0, q, 0, -q^(-1), 0, 0, 0, 0, -q^(-1)}, {0, 0, q, -1, 0, 0, 0, 0, 0}, {0, 0, 0, -q^3, 0, 0, 0, 0, 0}, {0, 0, 0, 0, q, 0, -q^(-1), 0, -1}, {0, 0, 0, 0, 0, q, -1, 0, 0}, {0, 0, 0, 0, 0, 0, -q^3, 0, 0}, {0, 0, 0, 0, 0, 0, 0, q, -1}, {0, 0, 0, 0, 0, 0, 0, 0, -q^3}}, {{q, 0, 0, 0, 0, 0, 0, 0, 0}, {0, q, 0, 0, 0, 0, 0, 0, 0}, {0, 0, q - q^3, q^2, 0, 0, 0, 0, 0}, {0, 0, q^2, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, q, 0, 0, 0, 0}, {0, 0, 0, 0, 0, q - q^3, q^2, 0, 0}, {0, 0, 0, 0, 0, q^2, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, q - q^3, q^2}, {0, 0, 0, 0, 0, 0, 0, q^2, 0}}, {{q, 0, 0, 0, 0, 0, 0, 0, -q^(-4)}, {0, q - q^3, q^2, 0, 0, 0, 0, 0, -q^(-3)}, {0, q^2, 0, 0, 0, 0, 0, 0, -q^(-2)}, {0, 0, 0, q, 0, 0, 0, 0, -q^(-1)}, {0, 0, 0, 0, q - q^3, q^2, 0, 0, -q^(-2)}, {0, 0, 0, 0, q^2, 0, 0, 0, -q^(-1)}, {0, 0, 0, 0, 0, 0, q, 0, -1}, {0, 0, 0, 0, 0, 0, 0, q, -1}, {0, 0, 0, 0, 0, 0, 0, 0, -q^3}}, {{q - q^3, q^2, 0, 0, 0, 0, 0, 0, 0}, {q^2, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, q, 0, 0, 0, 0, 0, 0}, {0, 0, 0, q, 0, 0, 0, 0, 0}, {0, 0, 0, 0, q, 0, 0, 0, 0}, {0, 0, 0, 0, 0, q - q^3, 0, q^2, 0}, {0, 0, 0, 0, 0, 0, q - q^3, 0, q^2}, {0, 0, 0, 0, 0, q^2, 0, 0, 0}, {0, 0, 0, 0, 0, 0, q^2, 0, 0}}, {{q, 0, 0, 0, 0, 0, 0, 0, 0}, {0, q - q^3, 0, 0, q^2, 0, 0, 0, 0}, {0, 0, q - q^3, 0, 0, q^2, 0, 0, 0}, {0, 0, 0, q - q^3, 0, 0, q^2, 0, 0}, {0, q^2, 0, 0, 0, 0, 0, 0, 0}, {0, 0, q^2, 0, 0, 0, 0, 0, 0}, {0, 0, 0, q^2, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, q, 0}, {0, 0, 0, 0, 0, 0, 0, 0, q}}}}}, {1 + q^(-4) + q^(-2) + q^2 + q^4, {{{{q^(-1), 0, 0, 0, -q^(-7)}, {0, q^(-1), 0, 0, -q^(-6)}, {0, 0, q^(-1), 0, -q^(-5)}, {0, 0, 0, q^(-1), -q^(-4)}, {0, 0, 0, 0, -q^(-3)}}, {{q^(-1), 0, 0, 0, 0}, {0, q^(-1), 0, 0, 0}, {0, 0, q^(-1), 0, 0}, {0, 0, 0, 0, q^(-2)}, {0, 0, 0, q^(-2), -((1 - q^2)/q^3)}}, {{q^(-1), 0, 0, 0, 0}, {0, q^(-1), 0, 0, 0}, {0, 0, 0, q^(-2), 0}, {0, 0, q^(-2), -((1 - q^2)/q^3), 0}, {0, 0, 0, 0, q^(-1)}}, {{q^(-1), 0, 0, 0, 0}, {0, 0, q^(-2), 0, 0}, {0, q^(-2), -((1 - q^2)/q^3), 0, 0}, {0, 0, 0, q^(-1), 0}, {0, 0, 0, 0, q^(-1)}}, {{0, q^(-2), 0, 0, 0}, {q^(-2), -((1 - q^2)/q^3), 0, 0, 0}, {0, 0, q^(-1), 0, 0}, {0, 0, 0, q^(-1), 0}, {0, 0, 0, 0, q^(-1)}}}, {{{q, 0, 0, 0, -q^(-3)}, {0, q, 0, 0, -q^(-2)}, {0, 0, q, 0, -q^(-1)}, {0, 0, 0, q, -1}, {0, 0, 0, 0, -q^3}}, {{q, 0, 0, 0, 0}, {0, q, 0, 0, 0}, {0, 0, q, 0, 0}, {0, 0, 0, q - q^3, q^2}, {0, 0, 0, q^2, 0}}, {{q, 0, 0, 0, 0}, {0, q, 0, 0, 0}, {0, 0, q - q^3, q^2, 0}, {0, 0, q^2, 0, 0}, {0, 0, 0, 0, q}}, {{q, 0, 0, 0, 0}, {0, q - q^3, q^2, 0, 0}, {0, q^2, 0, 0, 0}, {0, 0, 0, q, 0}, {0, 0, 0, 0, q}}, {{q - q^3, q^2, 0, 0, 0}, {q^2, 0, 0, 0, 0}, {0, 0, q, 0, 0}, {0, 0, 0, q, 0}, {0, 0, 0, 0, q}}}}}, {1 + q^(-6) + q^(-4) + q^(-2) + q^2 + q^4 + q^6, {{{{q^(-1)}}, {{q^(-1)}}, {{q^(-1)}}, {{q^(-1)}}, {{q^(-1)}}}, {{{q}}, {{q}}, {{q}}, {{q}}, {{q}}}}}}</div>

69.110.6.1