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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
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.
Received: 30.11.2017 Revised: 30.11.2017
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
Linking options:
https://www.mathnet.ru/eng/tmf9517https://doi.org/10.4213/tmf9517 https://www.mathnet.ru/eng/tmf/v198/i2/p246
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Abstract page: | 275 | Full-text PDF : | 52 | References: | 20 | First page: | 3 |
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