| Résume |
The (deformed) Harish-Chandra isomorphism relates a
quantization of the Hilbert scheme of points on the plane and the
spherical subalgebra of the rational Cherednik algebra for the
symmetric group. This relationship allows a rich interplay between
coherent sheaves on the HIlbert scheme and modules for the Cherednik
algebra. I will discuss a q-deformation of this story, wherein the
quantized Hilbert scheme is replaced with a quantized multiplicative
quiver variety (as defined by Varagnolo--Vasserot and Jordan) and the
rational Cherednik algebra is replaced with the double affine Hecke
algebra (DAHA). A key feature of proving an analogous isomorphism is to
use an idea of Varagnolo--Vasserot involving the Etingof--Kirillov
realization of Macdonald polynomials via intertwiners. If time permits,
I will say a few things about a cyclotomic version of this isomorphism.
For the first part of the talk, I will give an introduction to the
ribbon category structure on finite dimension modules for the quantized
enveloping algebra. |
