Kashiwara Algebras and Imaginary Verma Modules for U_q(\mathfrakg)

2013/08/08 by Cox, Ben, Futorny, Vyacheslav, Misra, Kailash C.
#FOS: Mathematics #Quantum Algebra (math.QA) #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.1308.1974

Abstract

We consider imaginary Verma modules for quantum affine algebra U_q(\mathfrakg), where \mathfrakg is of type 1 i.e. of non-twisted type, and construct Kashiwara type operators and the Kashiwara algebra \mathcal K_q. We show that a certain quotient \mathcal N_q^- of U_q(\mathfrakg) is a simple \mathcal K_q-module.

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