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Quantizations of character varieties and double affine Hecke algebras

Peter Samuelson
(University of Toronto)
Seminar
Friday, 1 August, 2014, at 14:15-15:15, in Aud. D3 (1531-215)
Abstract:

The skein module of the complement of a knot $K$ can be viewed as a quantization of the character variety of $S^3 \ K$. It is a module over the double affine Hecke algebra (at $t=1$), and it also determines classical polynomial invariants of the knot $K$. We will explain this, and give examples of how representation-theoretic statements on the DAHA side translate into statements about knot invariants. In particular, a representation-theoretic conjecture implies (for each $n$) the existence of a 3-variable polynomial knot invariant that specializes to the $n$'th colored Jones polynomials of $K$. (This is joint work with Yuri Berest.)

Organised by: QGM
Contact person: Jørgen Ellegaard Andersen