Theoretical and Mathematical Physics

, Volume 198, Issue 2, pp 215–238 | Cite as

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

  • I. C.-H. IpEmail author


our previous work, we studied positive representations of split real quantum groups \(\mathcal{U}_{q\widetilde{q}}(\mathfrak{g}_\mathbb{R})\) 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.


positive representation split real quantum group modular double quantum cluster algebra tensor category 


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© Pleiades Publishing, Ltd. 2019

Authors and Affiliations

  1. 1.Department of MathematicsHong Kong University of Science and TechnologyHong KongChina

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