From Schur-Weyl duality to quantum symmetric pairs
Date/Time:14 Jan 2019 15:00
Venue: S17 #04-05 SR2
Speaker: Bao Huanchen, University of Maryland (College Park)
From Schur-Weyl duality to quantum symmetric pairs
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-Weyl duality to other classical types. This new duality leads to a theory of canonical bases arising from quantum symmetric pairs generalizing Lusztig’s canonical bases on quantum groups.
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