Representations and Lie Theory Seminar

Spring 2020

Time: Wednesday, 16:15 - 17:15
Location: MW 154

Schedule of talks:


January 22 Yiqiang Li Geometric Schur duality ABC
February 12 Andrei Negut On the quantum toroidal algebra in type A
February 19
February 26 Corey Jones Groups acting on affine buildings and An spiders in positive characteristic
March 11 No Seminar Spring Break

Seminar cancelled due to viral outbreak


January 22. Schur duality serves as a bridge relating the representation theories of symmetric groups and general linear groups. The duality and its quantization admit a geometric realization via flag varieties of type A. We shall present this construction in this talk and its classical analogues which relate isotropic flag varieties with the coideal subalgeba, and its quantization, in a quasi-split symmetric pair of a general linear Lie algebra. This is a joint work with H. Bao, J. Kujawa and W. Wang.

February 12. Quantum toroidal algebras are affinizations of quantum affine groups, and we will consider the type A version of this construction. We will define various features of this object, such as a PBW basis, a new Hopf algebra structure, and (time permitting) connections with moduli spaces of sheaves on surfaces.

February 26. An spiders are graphically defined monoidal categories that describe the representation theory of (quantum) sln+1. As such, they come equipped with a standard realization inside the monoidal category of finite dimensional vector spaces (called a fiber functor). However, it is very interesting to find more exotic fiber functors, yielding new Hopf algebras and interesting solutions to the Yang-Baxter equations. In this talk, we will explain a construction of exotic fiber functors for classical An in positive characteristic arising from groups acting freely and transitively on the vertices of a building of type affine An.

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