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On Tensor Products of Positive Representations of Split Real Quantum Borel Subalgebra Uqq (bℝ)

Ivan Chi-Ho Ip HKUST

Quantum Algebra mathscidoc:1909.43015

Transactions of the American Mathematical Society, 370, (6)
We study the positive representations Pλ of split real quantum groups Uqq (gℝ) restricted to the Borel subalgebra Uqq (bℝ). We prove that the restriction is independent of the parameter λ. Furthermore, we prove that it can be constructed from the GNS-representation of the multiplier Hopf algebra UqqC ∗ (b ℝ) defined earlier, which allows us to decompose their tensor product using the theory of the “multiplicative unitary”. In particular, the quantum mutation operator can be constructed from the multiplicity module, which will be an essential ingredient in the construction of quantum higher Teichmüller theory from the perspective of representation theory, generalizing earlier work by Frenkel-Kim.
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@inproceedings{ivanon,
  title={On Tensor Products of Positive Representations of Split Real Quantum Borel Subalgebra Uqq (bℝ)},
  author={Ivan Chi-Ho Ip},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20190923151940714432506},
  booktitle={Transactions of the American Mathematical Society},
  volume={370},
  number={6},
}
Ivan Chi-Ho Ip. On Tensor Products of Positive Representations of Split Real Quantum Borel Subalgebra Uqq (bℝ). Vol. 370. In Transactions of the American Mathematical Society. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20190923151940714432506.
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