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Teoreticheskaya i Matematicheskaya Fizika, 2019, Volume 198, Number 2, Pages 246–272
DOI: https://doi.org/10.4213/tmf9517
(Mi tmf9517)
 

Cluster realization of positive representations of a split real quantum Borel subalgebra

I. Ch.-H. Ip

Department of Mathematics, Hong Kong University of Science and Technology, Hong Kong
References:
Abstract: In our previous work, we studied positive representations of split real quantum groups $\mathcal U_{q\tilde q}(\mathfrak g_{\mathbb R})$ 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.
Keywords: positive representation, split real quantum group, modular double, quantum cluster algebra, tensor category.
Funding agency Grant number
Ministry of Education, Culture, Sports, Science and Technology, Japan
Japan Society for the Promotion of Science JP16K17571
This research is supported by the Top Global University Project, MEXT, Japan of Kyoto University and JSPS KAKENHI (Grant No. JP16K17571).
Received: 30.11.2017
Revised: 30.11.2017
English version:
Theoretical and Mathematical Physics, 2019, Volume 198, Issue 2, Pages 215–238
DOI: https://doi.org/10.1134/S0040577919020041
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: I. Ch.-H. Ip, “Cluster realization of positive representations of a split real quantum Borel subalgebra”, TMF, 198:2 (2019), 246–272; Theoret. and Math. Phys., 198:2 (2019), 215–238
Citation in format AMSBIB
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\paper Cluster realization of positive representations of a~split real quantum Borel subalgebra
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    Теоретическая и математическая физика Theoretical and Mathematical Physics
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