Based morphisms for characters of quantum symmetric pairs
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866915565288816640 |
|---|---|
| author | Meereboer, Stein |
| author_facet | Meereboer, Stein |
| contents | We study based one-dimensional modules of quantum symmetric pairs over the field $\mathbb{Q}(q)$. We provide a complete classification of one-dimensional $\mathbf{B}$-modules that appear as submodules of simple finite-dimensional based $\mathbf{U}$-modules and determine the corresponding branching rules. The main result of this paper shows that the corresponding projections are morphisms of based $\mathbf{B}$-modules. To this end we characterize one-dimensional modules at $q=\infty$, thus developing a $\imath$crystal basis theory for these modules. This is then applied to show compatibility with the integral forms of the (dual-)canonical basis. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_17655 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Based morphisms for characters of quantum symmetric pairs Meereboer, Stein Quantum Algebra 17B37 We study based one-dimensional modules of quantum symmetric pairs over the field $\mathbb{Q}(q)$. We provide a complete classification of one-dimensional $\mathbf{B}$-modules that appear as submodules of simple finite-dimensional based $\mathbf{U}$-modules and determine the corresponding branching rules. The main result of this paper shows that the corresponding projections are morphisms of based $\mathbf{B}$-modules. To this end we characterize one-dimensional modules at $q=\infty$, thus developing a $\imath$crystal basis theory for these modules. This is then applied to show compatibility with the integral forms of the (dual-)canonical basis. |
| title | Based morphisms for characters of quantum symmetric pairs |
| topic | Quantum Algebra 17B37 |
| url | https://arxiv.org/abs/2510.17655 |