Elliptic Schur-Weyl duality and representations of the DAHA

Abstract: Building on the work of Calaque-Enriquez-Etingof, Lyubashenko-Majid, and Arakawa-Suzuki, Jordan constructed a functor from quantum D-modules on special linear groups to representations of the double affine Hecke algebra (DAHA) in type A. When we input quantum functions on GL(N) the output is L(k^N), the irreducible DAHA representation indexed by an N by k rectangle. For the specified parameters, L(k^N) is Y-semisimple, i.e. one can diagonalize the Dunkl operators. We give an explicit combinatorial description of this module via its Y-weight basis in terms of skew tableaux, or equivalently, periodic tableaux of rectangular shape. This is joint work with David Jordan. If time allows, I will talk about work in progress with Sam Gunningham and David Jordan on the quantum Hotta-Kashiwara D-modules, their endomorphim algebras, and which DAHA representations they become after applying Jordan's elliptic Schur-Weyl functor.

mathematical physicsalgebraic geometrycategory theoryrepresentation theory

Audience: researchers in the topic

UMass Amherst Representation theory seminar