Weyl algebras for quantum homogeneous spaces
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2022
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| _version_ | 1866909209527844864 |
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| author | Letzter, Gail Sahi, Siddhartha Salmasian, Hadi |
| author_facet | Letzter, Gail Sahi, Siddhartha Salmasian, Hadi |
| contents | We present a new family of quantum Weyl algebras where the polynomial part is the quantum analog of functions on homogeneous spaces corresponding to symmetric matrices, skew symmetric matrices, and the entire space of matrices of a given size. The construction uses twisted tensor products and their deformations combined with invariance properties derived from quantum symmetric pairs. These quantum Weyl algebras admit $U_q(\mathfrak{gl}_N)$-module algebra structures compatible with standard ones on the polynomial part, have relations that are expressed nicely via matrices, and are closely related to an algebra arising in the theory of quantum bounded symmetric domains. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2211_03833 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Weyl algebras for quantum homogeneous spaces Letzter, Gail Sahi, Siddhartha Salmasian, Hadi Quantum Algebra Rings and Algebras Representation Theory 17B37, 20G42 We present a new family of quantum Weyl algebras where the polynomial part is the quantum analog of functions on homogeneous spaces corresponding to symmetric matrices, skew symmetric matrices, and the entire space of matrices of a given size. The construction uses twisted tensor products and their deformations combined with invariance properties derived from quantum symmetric pairs. These quantum Weyl algebras admit $U_q(\mathfrak{gl}_N)$-module algebra structures compatible with standard ones on the polynomial part, have relations that are expressed nicely via matrices, and are closely related to an algebra arising in the theory of quantum bounded symmetric domains. |
| title | Weyl algebras for quantum homogeneous spaces |
| topic | Quantum Algebra Rings and Algebras Representation Theory 17B37, 20G42 |
| url | https://arxiv.org/abs/2211.03833 |