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Positive Casimir and Central Characters of Split Real Quantum Groups

Ivan Chi-Ho Ip The University of Tokyo

Quantum Algebra mathscidoc:1811.43004

Distinguished Paper Award in 2018

Communications in Mathematical Physics, 2016
We describe the generalized Casimir operators and their actions on the positive representations Pλ of the modular double of split real quantum groups Uqq (gR). We introduce the notion of virtual highest and lowest weights, and show that the central characters admit positive values for all parameters λ. 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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@inproceedings{ivan2016positive,
  title={Positive Casimir and Central Characters of Split Real Quantum Groups},
  author={Ivan Chi-Ho Ip},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20181126095546285805181},
  booktitle={Communications in Mathematical Physics},
  year={2016},
}
Ivan Chi-Ho Ip. Positive Casimir and Central Characters of Split Real Quantum Groups. 2016. In Communications in Mathematical Physics. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20181126095546285805181.
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