/ Joshua Wen: The quantum Harish-Chandra homomorphism for GL_n

Joshua Wen: The quantum Harish-Chandra homomorphism for GL_n

April 19, 2022
4:30 pm - 5:30 pm

Abstract: This talk is about comparing two a priori different quantizations of the GL_n-character variety for the torus. One of them is the spherical double affine Hecke algebra at q=t. The other is the combinatorial quantization defined by Alekseev, Grosse, and Schomerus, which has also reappeared in works of Varagnolo-Vasserot and Jordan. The latter has also appeared in works of Ben-Zvi, Brochier, and Jordan applying factorization homology to the E_2 category of finite-dimensional representations of quantum enveloping algebras to obtain categorical invariants of topological surfaces. Conjecturally, both algebras are isomorphic. However, neither algebra possesses a presentation via generators and relations, and I will present a way to compare the two via an action on characters for GL_n. This approach has a natural t-deformation wherein the characters are replaced with Macdonald polynomials.