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Quantizations of character varieties and double affine Hecke algebras

Peter Samuelson
(University of Toronto)
Seminar
Fredag, 1 august, 2014, at 14:15-15:15, in Aud. D3 (1531-215)
Abstrakt:

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.)

Organiseret af: QGM
Kontaktperson: Jørgen Ellegaard Andersen