Representation theory of mirabolic quantum $\mathfrak{sl}_n$
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866911653736480768 |
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| author | Goyal, Pallav Rosso, Daniele |
| author_facet | Goyal, Pallav Rosso, Daniele |
| contents | We show that the mirabolic quantum group $MU(n)$ is a comodule algebra over the quantized enveloping algebra $U_v(\mathfrak{sl}_n)$, and use this structure to give a complete classification of its finite dimensional representations. In particular, we explicitly describe the construction of all irreducible finite dimensional representations of $MU(n)$ and show that the category of finite dimensional representations is semisimple. A crucial step involves constructing and analyzing Verma-type universal representations of $MU(n)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_07469 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Representation theory of mirabolic quantum $\mathfrak{sl}_n$ Goyal, Pallav Rosso, Daniele Representation Theory Quantum Algebra Rings and Algebras We show that the mirabolic quantum group $MU(n)$ is a comodule algebra over the quantized enveloping algebra $U_v(\mathfrak{sl}_n)$, and use this structure to give a complete classification of its finite dimensional representations. In particular, we explicitly describe the construction of all irreducible finite dimensional representations of $MU(n)$ and show that the category of finite dimensional representations is semisimple. A crucial step involves constructing and analyzing Verma-type universal representations of $MU(n)$. |
| title | Representation theory of mirabolic quantum $\mathfrak{sl}_n$ |
| topic | Representation Theory Quantum Algebra Rings and Algebras |
| url | https://arxiv.org/abs/2510.07469 |