Symmetries for spherical functions of type $χ$ for quantum symmetric pairs
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866913706368040960 |
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| author | Meereboer, Stein |
| author_facet | Meereboer, Stein |
| contents | Let $\mathfrak{g}$ be a complex semisimple Lie algebra and let $\mathbf{U}_q(\mathfrak{g})$ denote the associated Drinfel'd Jimbo quantized enveloping algebra. In this paper we study spherical functions of $\mathbf{U}_q(\mathfrak{g})$ related to characters. We show invariance under the Wang-Zhang braid group operators and show relative Weyl group invariance, when restricted to the quantum torus. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_15401 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Symmetries for spherical functions of type $χ$ for quantum symmetric pairs Meereboer, Stein Representation Theory Quantum Algebra 43 Let $\mathfrak{g}$ be a complex semisimple Lie algebra and let $\mathbf{U}_q(\mathfrak{g})$ denote the associated Drinfel'd Jimbo quantized enveloping algebra. In this paper we study spherical functions of $\mathbf{U}_q(\mathfrak{g})$ related to characters. We show invariance under the Wang-Zhang braid group operators and show relative Weyl group invariance, when restricted to the quantum torus. |
| title | Symmetries for spherical functions of type $χ$ for quantum symmetric pairs |
| topic | Representation Theory Quantum Algebra 43 |
| url | https://arxiv.org/abs/2405.15401 |