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SUMMARY:Representations of shifted affine quantum groups and Coulomb branc
 hes - Michela Varagnolo (Université de Cergy-Pontoise)
DTSTART:20250717T083000Z
DTEND:20250717T093000Z
UID:TALK234007@talks.cam.ac.uk
DESCRIPTION:I will present an equivalence between the category O for shift
 ed quantum loop groups (associated witharbitrary Cartan matrices\, includi
 ng non-symmetric ones) and a module category over a new type of quiverHeck
 e algebra. This equivalence is based on the computation of the K-theoretic
  analogue of Coulombbranches with symmetrizers introduced by Nakajima and 
 Weekes. At the decategorified level\, this yields aconnection between the 
 Grothendieck group of O and a finite-dimensional module over a simple Lie 
 algebraof unfolded symmetric type. In some cases\, this module can be comp
 uted explicitly\; more generally\, one candescribe its crystal structure v
 ia a combinatorial rule. Joint with Eric Vasserot.
LOCATION:External
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