Stieltjes-Wigert and quantum topological invariants
Seminar Room 1, Newton Institute
We introduce the Stieltjes-Wigert polynomials and show their utility in the analytical computation of quantum topological invariants. Examples are given, the simplest being the computation of the Witten-Reshetikhin-Turaev invariant. The computation of quantum dimensions, presented in detail, requires an interesting mixture of Stieltjes-Wigert polynomials and key results borrowed from algebraic combinatorics. The relationship with random matrices and the relevance of other set of polynomials, such as the biorthogonal version of the Sieltjes-Wigert polynomials is also discussed.