QuantumGroups`

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Download

For now, QuantumGroups` is only available from its SVN repository (about SVN), or as a subpackage of KnotTheory` (although it's not yet in the publically available version).

Installation

If you're using QuantumGroup` from inside KnotTheory`, you shouldn't have to do anything. Otherwise, add it to the path (that is, add the directory containing QuantumGroups.m to $Path), and execute <<QuantumGroups`.

Examples of use

Root systems

Weyl groups

Weight multiplicities and tensor product decomposition

Explicit bases, and matrix presentations

Generators and relations of quantum groups

Action of the braided coxeter group on the quantum group

Quantum root operators

R-matrices

Quantum knot invariants

Things to do

  • PBW basis for the quantum group
  • Special bases for representations
    • Gelfand-Tsetlin basis for type A
    • Canonical bases
    • Web bases for , , ,