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Positive Representations of Non-simply-laced Split Real Quantum Groups

Ivan Chi-Ho Ip UST

Quantum Algebra mathscidoc:1909.43009

Journal of Algebra, 425, 2015
We construct the positive principal series representations for Uq(gR) where g is of type Bn, Cn, F4 or G2, parametrized by Rn where n is the rank of g. We show that under the representations, the generators of the Langlands dual group Uq(LgR) are related to the generators of Uq(gR) by the transcendental relations. This gives a new and very simple analytic relation between the Langlands dual pair. We define the modified quantum group Uqq(gR)=Uq(gR) ⊗ Uq(LgR) 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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@inproceedings{ivan2015positive,
  title={Positive Representations of Non-simply-laced Split Real Quantum Groups},
  author={Ivan Chi-Ho Ip},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20190920161728389477499},
  booktitle={Journal of Algebra},
  volume={425},
  year={2015},
}
Ivan Chi-Ho Ip. Positive Representations of Non-simply-laced Split Real Quantum Groups. 2015. Vol. 425. In Journal of Algebra. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20190920161728389477499.
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