## Representation Theory and Mathematical Physics Seminar: An elliptic Schur-Weyl construction of the rectangular representation of the DAHA

Seminar | September 6 | 4-5 p.m. | 939 Evans Hall

Monica Vazirani, UC Davis

Department of Mathematics

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.

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