Trace decategorification of tensor product algebras

2019/03/20 by Leonard, Christopher, Reeks, Michael
#FOS: Mathematics #Quantum Algebra (math.QA) #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.1903.08697

Abstract

We show that in ADE type the trace of Webster's categorification of a tensor product of irreducibles for the quantum group is isomorphic to a tensor product of Weyl modules for the current algebra U(\mathfrakg[t]). This extends a result of Beliakova, Habiro, Lauda, and Webster who showed that the trace of the categorified quantum group U^*(\mathfrakg) is isomorphic to U(\mathfrakg[t]), and the trace of a cyclotomic quotient of U^*(\mathfrakg), which categorifies a single irreducible for the quantum group, is isomorphic to a Weyl module for U(\mathfrakg[t]). We use a deformation argument based on Webster's technique of unfurling 2-representations.

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