Representations of shifted affine quantum groups and Coulomb branches

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• Michela Varagnolo (Université de Cergy-Pontoise)
• Thursday 17 July 2025, 09:30-10:30
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GCLW01 - Modular Lie theory

I will present an equivalence between the category O for shifted quantum loop groups (associated witharbitrary Cartan matrices, including non-symmetric ones) and a module category over a new type of quiverHecke 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 computed explicitly; more generally, one candescribe its crystal structure via a combinatorial rule. Joint with Eric Vasserot.

This talk is part of the Isaac Newton Institute Seminar Series series.

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