2-categorical affine symmetries of quantum enveloping algebras
Sam Qunell

TL;DR
This paper constructs 2-representations of affine quantum enveloping algebras' positive parts, extending known representations and relating to evaluation morphisms, with implications for character formulas.
Contribution
It introduces new 2-representations for affine quantum groups, extending existing frameworks and establishing connections to evaluation morphisms and prefundamental representations.
Findings
Constructed 2-representations for affine quantum groups in type A_n.
Extended the right-multiplication 2-representation to affine cases.
Provided new proofs for prefundamental representation character formulas.
Abstract
We produce 2-representations of the positive part of affine quantum enveloping algebras on their finite-dimensional counterparts in type . These 2-representations naturally extend the right-multiplication 2-representation of 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 and . We also show that a certain quotient of our 1-representation in type is isomorphic to a prefundamental representation. We use this to provide a new proof of the prefundamental representation character formulas in these cases.
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