Quantum Schur-Weyl duality and twisted torus knots

Roland van der Veen, KdV Institute, University of Amsterdam

Abstract: We introduce Schur-Weyl duality and its quantum counterpart, which shows how to decompose the tensor power of a representation in a symmetric way. Applying this technique in the case of quantum sl_2 a yields a basis that is well suited for dealing with the colored Jones invariant of generalized twist regions. We will show how the resulting formulas can help finding formulas for the Jones polynomial of (twisted) torus knots.