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| Main Author: | |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2502.19232 |
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| _version_ | 1866916631938072576 |
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| author | Meereboer, Stein |
| author_facet | Meereboer, Stein |
| contents | The theory of quantum symmetric pairs is applied to $q$-special functions. Previous work shows the existence of a family $χ$-spherical functions indexed by the integers for each Hermitian quantum symmetric pair. A distinguished family of such functions, invariant under the Weyl group of the restricted roots, is shown to be a family of Macdonald-Koornwinder polynomials if the restricted root system is reduced or if the Satake diagram is of type $\mathsf{AIII_a}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_19232 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Quantum spherical functions of type $χ$ as Macdonald-Koornwinder polynomials Meereboer, Stein Representation Theory Quantum Algebra 43 The theory of quantum symmetric pairs is applied to $q$-special functions. Previous work shows the existence of a family $χ$-spherical functions indexed by the integers for each Hermitian quantum symmetric pair. A distinguished family of such functions, invariant under the Weyl group of the restricted roots, is shown to be a family of Macdonald-Koornwinder polynomials if the restricted root system is reduced or if the Satake diagram is of type $\mathsf{AIII_a}$. |
| title | Quantum spherical functions of type $χ$ as Macdonald-Koornwinder polynomials |
| topic | Representation Theory Quantum Algebra 43 |
| url | https://arxiv.org/abs/2502.19232 |