Positive representations of non-simply-laced split real quantum groups

2012/05/14 by Ip, Ivan Chi-Ho
#FOS: Mathematics #Quantum Algebra (math.QA) #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.1205.2940

Abstract

We construct the positive principal series representations for U_q(g_R) where g is of type B_n, C_n, F₄ or G₂, parametrized by R^r where r is the rank of g. We show that under the representations, the generators of the Langlands dual group U_q(^Lg_R) are related to the generators of U_q(g_R) by the transcendental relations. We define the modified quantum group of the modular double and show that the representations of both parts of the modular double commute with each other, and there is an embedding into the q-tori polynomials.

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