Representation theory of the Reflection Equation Algebra II: Theory of shapes
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866913416449359872 |
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| author | De Commer, Kenny Moore, Stephen T. |
| author_facet | De Commer, Kenny Moore, Stephen T. |
| contents | We continue our study of the representations of the Reflection Equation Algebra (=REA) on Hilbert spaces, focusing again on the REA constructed from the $R$-matrix associated to the standard $q$-deformation of $GL(N,\mathbb{C})$ for $0<q<1$. We consider the Poisson structure appearing as the classical limit of the $R$-matrix, and parametrize the symplectic leaves explicitly in terms of a type of matrix we call a shape matrix. We then introduce a quantized version of the shape matrix for the REA, and show that each irreducible representation of the REA has a unique shape. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_03613 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Representation theory of the Reflection Equation Algebra II: Theory of shapes De Commer, Kenny Moore, Stephen T. Quantum Algebra Representation Theory We continue our study of the representations of the Reflection Equation Algebra (=REA) on Hilbert spaces, focusing again on the REA constructed from the $R$-matrix associated to the standard $q$-deformation of $GL(N,\mathbb{C})$ for $0<q<1$. We consider the Poisson structure appearing as the classical limit of the $R$-matrix, and parametrize the symplectic leaves explicitly in terms of a type of matrix we call a shape matrix. We then introduce a quantized version of the shape matrix for the REA, and show that each irreducible representation of the REA has a unique shape. |
| title | Representation theory of the Reflection Equation Algebra II: Theory of shapes |
| topic | Quantum Algebra Representation Theory |
| url | https://arxiv.org/abs/2407.03613 |