Affine $\mathrm{i}$quantum groups and Steinberg varieties of type C, II
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| Format: | Preprint |
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2026
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| _version_ | 1866917479256686592 |
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| author | Luo, Li Su, Changjian Xu, Zheming |
| author_facet | Luo, Li Su, Changjian Xu, Zheming |
| contents | A geometric realization of the quasi-split affine iquantum group of type $\mathrm{AIII}_{2n-1}^{(τ)}$ was given by Wang and the second author, in terms of equivariant K-groups of Steinberg varieties of type C. As a completion of that work, this paper focuses on the previously untreated case. We provide a similar construction of the quasi-split affine iquantum group of type $\mathrm{AIII}_{2n}^{(τ)}$, using the same equivariant K-groups of Steinberg varieties of type C. In the appendix, we employ Steinberg varieties of type D to give a new realization of the quasi-split affine iquantum group of type $\mathrm{AIII}_{2n-1}^{(τ)}$, thereby avoiding the localization method adopted in the previous work. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2605_09589 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Affine $\mathrm{i}$quantum groups and Steinberg varieties of type C, II Luo, Li Su, Changjian Xu, Zheming Quantum Algebra Representation Theory A geometric realization of the quasi-split affine iquantum group of type $\mathrm{AIII}_{2n-1}^{(τ)}$ was given by Wang and the second author, in terms of equivariant K-groups of Steinberg varieties of type C. As a completion of that work, this paper focuses on the previously untreated case. We provide a similar construction of the quasi-split affine iquantum group of type $\mathrm{AIII}_{2n}^{(τ)}$, using the same equivariant K-groups of Steinberg varieties of type C. In the appendix, we employ Steinberg varieties of type D to give a new realization of the quasi-split affine iquantum group of type $\mathrm{AIII}_{2n-1}^{(τ)}$, thereby avoiding the localization method adopted in the previous work. |
| title | Affine $\mathrm{i}$quantum groups and Steinberg varieties of type C, II |
| topic | Quantum Algebra Representation Theory |
| url | https://arxiv.org/abs/2605.09589 |