##### Department of Mathematics,

University of California San Diego

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### Math 295 - Mathematics Colloquium

## Huanchen Bao

## From Schur duality to quantum symmetric pairs

##### Abstract:

The classical Schur(-Weyl) duality relates the representation theory of general linear Lie algebras and symmetric groups. Drinfeld and Jimbo independently introduced quantum groups in their study of exactly solvable models, which leads to a quantization of the Schur duality relating quantum groups of general linear Lie algebras and Hecke algebras of symmetric groups. In this talk, I will explain the generalization of the (quantized) Schur duality to other classical types, algebraically, geometrically, and categorically. This new duality leads to a theory of canonical bases arising from quantum symmetric pairs generalizing Lusztigâ€™s canonical bases on quantum groups.

### November 27, 2018

### 3:00 PM

### AP&M 6402

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