The Capelli eigenvalue problem for quantum groups
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2022
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| _version_ | 1866929355570020352 |
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| author | Letzter, Gail Sahi, Siddhartha Salmasian, Hadi |
| author_facet | Letzter, Gail Sahi, Siddhartha Salmasian, Hadi |
| contents | We introduce and study quantum Capelli operators inside newly constructed quantum Weyl algebras associated to three families of symmetric pairs. Both the center of a particular quantized enveloping algebra and the Capelli operators act semisimply on the polynomial part of these quantum Weyl algebras. We show how to transfer well-known properties of the center arising from the theory of quantum symmetric pairs to the Capelli operators. Using this information, we provide a natural realization of Knop-Sahi interpolation polynomials as functions that produce eigenvalues for quantum Capelli operators. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2211_03838 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | The Capelli eigenvalue problem for quantum groups Letzter, Gail Sahi, Siddhartha Salmasian, Hadi Quantum Algebra Combinatorics Representation Theory 17B37, 20G42 We introduce and study quantum Capelli operators inside newly constructed quantum Weyl algebras associated to three families of symmetric pairs. Both the center of a particular quantized enveloping algebra and the Capelli operators act semisimply on the polynomial part of these quantum Weyl algebras. We show how to transfer well-known properties of the center arising from the theory of quantum symmetric pairs to the Capelli operators. Using this information, we provide a natural realization of Knop-Sahi interpolation polynomials as functions that produce eigenvalues for quantum Capelli operators. |
| title | The Capelli eigenvalue problem for quantum groups |
| topic | Quantum Algebra Combinatorics Representation Theory 17B37, 20G42 |
| url | https://arxiv.org/abs/2211.03838 |