Colored Jones polynomials and double affine Hecke algebras

Geometry Topology Seminar
Monday, November 11, 2013 - 14:00
1 hour (actually 50 minutes)
Skiles 006
University of Toronto
Frohman and Gelca showed that the Kauffman bracket skein module of the thickened torus is the Z_2 invariant subalgebra A'_q of the quantum torus A_q. This shows that the Kauffman bracket skein module of a knot complement is a module over A'_q. We discuss a conjecture that this module is naturally a module over the double affine Hecke algebra H, which is a 3-parameter family of algebras which specializes to A'_q. We give some evidence for this conjecture and then discuss some corollaries. If time permits we will also discuss a related topological construction of a 2-parameter family of H-modules associated to a knot in S^3. (All results in this talk are joint with Yuri Berest.)