Representations of shifted affine quantum groups and Coulomb branches

2025/03/08 by Varagnolo, Michela, Vasserot, Eric · 3 citations
#FOS: Mathematics #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.2503.06262

Abstract

We compare the integral category O of shifted affine quantum groups of symmetric and non symmetric types. To do so we compute the K-theoretic analog of the Coulomb branches with symmetrizers introduced by Nakajima and Weekes. This yields an equivalence of the category O with a module category over a new type of quiver Hecke algebras. At the decategorified level, this establishes a connection between the Grothendieck group of O and a finite-dimensional module over a simple Lie algebra of unfolded symmetric type. We compute this module in certain cases and give a combinatorial rule for its crystal.

Cited by

• Slant sums of quiver gauge theories
• Representations and characters of quantum affine algebras at the crossroads between cluster categorification and quantum integrable models
• Quantum cluster algebras and representations of shifted quantum affine algebras

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