2-categorical affine symmetries of quantum enveloping algebras

2025/02/12 by Qunell, Sam · 2 citations
#81R50 (Primary) 17B37 (Secondary) #FOS: Mathematics #Quantum Algebra (math.QA) #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.2502.08039

Abstract

We produce 2-representations of the positive part of affine quantum enveloping algebras on their finite-dimensional counterparts in type A_n. These 2-representations naturally extend the right-multiplication 2-representation of U_q⁺(\mathfraksl_n+1) on itself and are closely related to evaluation morphisms of quantum groups. We expect that our 2-representation exists in all simple types and show that the corresponding 1-representation exists in types D₄ and C₂. We also show that a certain quotient of our 1-representation in type A_n is isomorphic to a prefundamental representation. We use this to provide a new proof of the prefundamental representation character formulas in these cases.

Cited by

• Unipotent quantum coordinate ring and minuscule prefundamental representations: twisted case
• Categorification of quantum boson algebras

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