Quantum $SL^+(N,\mathbb{R})$ as a locally compact quantum group
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866912789158690816 |
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| author | De Commer, K. Schrader, G. Shapiro, A. Voigt, C. |
| author_facet | De Commer, K. Schrader, G. Shapiro, A. Voigt, C. |
| contents | We construct the first examples of purely continuous, $q$-deformed Lie type locally compact quantum groups in higher rank. They arise from Drinfeld-Jimbo quantization, at unimodular deformation parameter, of the totally positive part of higher rank split real Lie groups in type $A$. Our techniques are based on quantum cluster theory, in particular as developed through the work of Fock and Goncharov. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_21579 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Quantum $SL^+(N,\mathbb{R})$ as a locally compact quantum group De Commer, K. Schrader, G. Shapiro, A. Voigt, C. Quantum Algebra Operator Algebras 46L67, 13F60, 17B37 We construct the first examples of purely continuous, $q$-deformed Lie type locally compact quantum groups in higher rank. They arise from Drinfeld-Jimbo quantization, at unimodular deformation parameter, of the totally positive part of higher rank split real Lie groups in type $A$. Our techniques are based on quantum cluster theory, in particular as developed through the work of Fock and Goncharov. |
| title | Quantum $SL^+(N,\mathbb{R})$ as a locally compact quantum group |
| topic | Quantum Algebra Operator Algebras 46L67, 13F60, 17B37 |
| url | https://arxiv.org/abs/2512.21579 |