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Cluster Realization of Positive Representations of a Split Real Quantum Borel Subalgebra

Ivan Chi-Ho Ip HKUST

Quantum Algebra mathscidoc:1909.43021

Theoretical and Mathematical Physics(Russian Federation), 198, (2), 215-238, 2019
In our previous work, we studied positive representations of split real quantum groups U q q~ (g R ) restricted to their Borel part and showed that they are closed under taking tensor products. But the tensor product decomposition was only constructed abstractly using the GNS representation of a C*-algebraic version of the Drinfeld–Jimbo quantum groups. Here, using the recently discovered cluster realization of quantum groups, we write the decomposition explicitly by realizing it as a sequence of cluster mutations in the corresponding quiver diagram representing the tensor product.
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@inproceedings{ivan2019cluster,
  title={Cluster Realization of Positive Representations of a Split Real Quantum Borel Subalgebra},
  author={Ivan Chi-Ho Ip},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20190923155419782308512},
  booktitle={Theoretical and Mathematical Physics(Russian Federation)},
  volume={198},
  number={2},
  pages={215-238},
  year={2019},
}
Ivan Chi-Ho Ip. Cluster Realization of Positive Representations of a Split Real Quantum Borel Subalgebra. 2019. Vol. 198. In Theoretical and Mathematical Physics(Russian Federation). pp.215-238. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20190923155419782308512.
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