Cyclic adjoint modules and their embeddings in quantized enveloping algebras
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866908988865511424 |
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| author | Bhattacharjee, Arnab |
| author_facet | Bhattacharjee, Arnab |
| contents | We study cyclic adjoint modules arising from the relative locally finite part of the adjoint action of a quantum Levi subalgebra on a quantized enveloping algebra. We classify embeddings of finite-dimensional irreducible modules inside of quantized enveloping algebra via cyclic generators and show that such realizations are in general non-unique, exhibiting infinite families in the cominuscule case. We also introduce a partial order on cyclic adjoint modules, characterize its minimal elements, and prove finite generation by irreducible submodules. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_24490 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Cyclic adjoint modules and their embeddings in quantized enveloping algebras Bhattacharjee, Arnab Quantum Algebra Primary: 17B37, Secondary: 17B10, 20G42 We study cyclic adjoint modules arising from the relative locally finite part of the adjoint action of a quantum Levi subalgebra on a quantized enveloping algebra. We classify embeddings of finite-dimensional irreducible modules inside of quantized enveloping algebra via cyclic generators and show that such realizations are in general non-unique, exhibiting infinite families in the cominuscule case. We also introduce a partial order on cyclic adjoint modules, characterize its minimal elements, and prove finite generation by irreducible submodules. |
| title | Cyclic adjoint modules and their embeddings in quantized enveloping algebras |
| topic | Quantum Algebra Primary: 17B37, Secondary: 17B10, 20G42 |
| url | https://arxiv.org/abs/2603.24490 |