The Witten-Reshetikhin-Turaev representation of the Kauffman skein algebra

TL;DR

This paper demonstrates that the Witten-Reshetikhin-Turaev representation of the Kauffman skein algebra at certain roots of unity is irreducible and calculates its classical shadow, advancing understanding in quantum topology.

Contribution

It proves irreducibility of the Witten-Reshetikhin-Turaev representation and computes its classical shadow for primitive roots of unity with odd N.

Findings

Representation is irreducible

Classical shadow is explicitly computed

Advances understanding of quantum invariants

Abstract

For A a primitive 2N-root of unity with N odd, the Witten-Reshetikhin-Turaev topological quantum field theory provides a representation of the Kauffman skein algebra of a closed surface. We show that this representation is irreducible and we compute its classical shadow, in the sense of earlier work of the authors (arXiv:1206.1638).