Affine quantum Schur algebras and $\imath$quantum groups with three parameters
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866914061419020288 |
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| author | Luo, Li Yu, Xirui |
| author_facet | Luo, Li Yu, Xirui |
| contents | We study the affine quantum Schur algebras corresponding to the affine Hecke algebras of type C with three parameters. Multiplication formulas for semisimple generators are derived for these algebras. We prove that they admit a stabilization property in the sense of Beilinson-Lusztig-MacPherson, by which we construct quasi-split $\imath$quantum groups of affine type AIII with three parameters. Upon specialization of parameters, we recover some known multiplication formulas for affine quantum Schur algebras of types C and D with equal parameters. We take this opportunity to demonstrate in the appendix that different forms of multiplication formulas for affine quantum Schur algebras of types C with equal parameters across the literature are indeed equivalent. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_23559 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Affine quantum Schur algebras and $\imath$quantum groups with three parameters Luo, Li Yu, Xirui Quantum Algebra Representation Theory We study the affine quantum Schur algebras corresponding to the affine Hecke algebras of type C with three parameters. Multiplication formulas for semisimple generators are derived for these algebras. We prove that they admit a stabilization property in the sense of Beilinson-Lusztig-MacPherson, by which we construct quasi-split $\imath$quantum groups of affine type AIII with three parameters. Upon specialization of parameters, we recover some known multiplication formulas for affine quantum Schur algebras of types C and D with equal parameters. We take this opportunity to demonstrate in the appendix that different forms of multiplication formulas for affine quantum Schur algebras of types C with equal parameters across the literature are indeed equivalent. |
| title | Affine quantum Schur algebras and $\imath$quantum groups with three parameters |
| topic | Quantum Algebra Representation Theory |
| url | https://arxiv.org/abs/2509.23559 |