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Lie Group Quantum Mathematics Seminar

Completing the A_2 Andrews-Schilling-Warnaar identities

Shashank Kanade, University of Denver

Location:  Zoom
Date & time: Friday, 15 April 2022 at 12:10PM - 1:10PM

Abstract Since the pioneering works of Lepowsky-Milne and Lepowsky-Wilson, affine Lie algebras have been an incredibly rich source of Rogers-Ramanujan-type identities. In a groundbreaking paper in 1999, Andrews-Schilling-Warnaar invented an A_2 generalization of the (A_1) Bailey lemma and discovered sum-side representations of principal characters for some (but not all!) standard A_2^{(1)} -modules. Recently, in a joint work with Matthew C. Russell, we have been able to complete their picture by providing conjectures encompassing all standard modules. We have proved our conjectures in some low levels, and proved some new identities in levels divisible by 3 (= dual Coxeter number of A_2^{(1)}). For this talk, my plan is to explain this picture and its relations to cylindric partitions, principal W-algebras, etc.

Zoom link
Meeting ID: 939 2146 5287
Passcode: 196884, the dimension of the weight 2 homogeneous
subspace of the moonshine module

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