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Gauss-lusztig Decomposition for Positive Quantum Groups and Representation by Q-tori

Ivan Chi-Ho Ip UST

Quantum Algebra mathscidoc:1909.43010

Journal of Pure and Applied Algebra, 219, 5650-5672, 2015
We found an explicit construction of a representation of the positive quantum group and its modular double by positive essentially self-adjoint operators. Generalizing Lusztig's parametrization, we found a Gauss type decomposition for the totally positive quantum group parametrized by the standard decomposition of the longest element . Under this parametrization, we found explicitly the relations between the standard quantum variables, the relations between the quantum cluster variables, and realizing them using non-compact generators of the q-tori by positive essentially self-adjoint operators. The modular double arises naturally from the transcendental relations, and an space in the von Neumann setting can also be defined.
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@inproceedings{ivan2015gauss-lusztig,
  title={Gauss-lusztig Decomposition for Positive Quantum Groups and Representation by Q-tori},
  author={Ivan Chi-Ho Ip},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20190920162934109147500},
  booktitle={Journal of Pure and Applied Algebra},
  volume={219},
  pages={5650-5672},
  year={2015},
}
Ivan Chi-Ho Ip. Gauss-lusztig Decomposition for Positive Quantum Groups and Representation by Q-tori. 2015. Vol. 219. In Journal of Pure and Applied Algebra. pp.5650-5672. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20190920162934109147500.
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