Affine $\imath$quantum groups and Steinberg varieties of type C
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866914619814051840 |
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| author | Su, Changjian Wang, Weiqiang |
| author_facet | Su, Changjian Wang, Weiqiang |
| contents | We provide a geometric realization of the quasi-split affine $\imath$quantum group of type AIII$_{2n-1}^{(τ)}$ in terms of equivariant K-groups of non-connected Steinberg varieties of type C. This uses a new Drinfeld type presentation of this affine $\imath$quantum group which admits very nontrivial Serre relations. We then construct à la Springer a family of finite-dimensional standard modules and irreducible modules of this $\imath$quantum group, and provide a composition multiplicity formula of the standard modules. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_06865 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Affine $\imath$quantum groups and Steinberg varieties of type C Su, Changjian Wang, Weiqiang Representation Theory Quantum Algebra We provide a geometric realization of the quasi-split affine $\imath$quantum group of type AIII$_{2n-1}^{(τ)}$ in terms of equivariant K-groups of non-connected Steinberg varieties of type C. This uses a new Drinfeld type presentation of this affine $\imath$quantum group which admits very nontrivial Serre relations. We then construct à la Springer a family of finite-dimensional standard modules and irreducible modules of this $\imath$quantum group, and provide a composition multiplicity formula of the standard modules. |
| title | Affine $\imath$quantum groups and Steinberg varieties of type C |
| topic | Representation Theory Quantum Algebra |
| url | https://arxiv.org/abs/2407.06865 |