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arXiv · 1503.00543

Positive Casimir and Central Characters of Split Real Quantum Groups

Ivan Chi-Ho Ip
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Abstract

We describe the generalized Casimir operators and their actions on the positive representations $P_{\lambda}$ of the modular double of split real quantum groups $U_{q\tilde{q}}(g_R)$. We introduce the notion of virtual highest and lowest weights, and show that the central characters admit positive values for all parameters $\lambda$. We show that their image defines a semi-algebraic region bounded by real points of the discriminant variety independent of $q$, and we discuss explicit examples in the lower rank cases.

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BibTeXRIS

Ivan Chi-Ho Ip. 2015-03-02. Positive Casimir and Central Characters of Split Real Quantum Groups. https://arxiv.org/abs/1503.00543

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