Title: An elliptic Schur-Weyl construction of the rectangular representation of the DAHA
Speaker: Monica Vazirani (UC Davis)
Abstract: Building on the work of Calaque-Enriquez-Etingof, Lyubashenko-Majid, and Arakawa-Suzuki, Jordan constructed a functor from quantum D-modules on general 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. This is joint work with David Jordan.
Seminar URL: https://research.math.osu.edu/reps/
