Pavel Etigof

Title: Cherednik algebras and torus knots

Abstract: The Cherednik algebra B(c,n), generated by symmetric polynomials
and the quantum Calogero-Moser Hamiltonian, appears in many areas of mathematics.
It depends on two parameters - the coupling constant c and number of variables n.
I will talk about representations of this algebra, and in particular about a mysterious
isomorphism between the representations of B(m/n,n) and B(n/m,m) of minimal functional
dimension. This symmetry between m and n is made manifest by the fact that the characters
of these representations can be expressed in terms of the colored HOMFLY polynomial
of the torus knot T(m/d,n/d), where d=GCD(m,n).

The talk is based on my joint work with E. Gorsky and I. Losev.