Generic Gelfand-Tsetlin Representations of U_q^tw(\mathfrakso₃) and U_q^tw(\mathfrakso₄)

2021/05/17 by Disch, Jordan
#FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Quantum Algebra (math.QA) #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.2105.08033

Abstract

We construct generic Gelfand-Tsetlin representations of the \imathquantum groups U_q^tw(\mathfrakso₃) and U_q^tw(\mathfrakso₄). These representations are infinite-dimensional analogs to the finite-dimensional irreducible representations provided by Gavrilik and Klimyk. They are quantum analogs of generic Gelfand-Tsetlin representations constructed by Mazorchuk. We give sufficient conditions for irreducibility and provide an upper bound for the length with the help of Casimir elements found by Molev, Ragoucy, and Sorba.

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