On the category $\mathcal{O}$ of a hybrid quantum group
Fuente:
arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2022
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| _version_ | 1866915063037689856 |
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| author | Situ, Quan |
| author_facet | Situ, Quan |
| contents | We study the representation theory of a hybrid quantum group at root of unity $ζ$ introduced by Gaitsgory. After discussing some basic properties of its category $\mathcal{O}$, we study deformations of the category $\mathcal{O}$. For subgeneric deformations, we construct the endomorphism algebra of big projective object and compute it explicitly. Our main result is an algebra isomorphism between the center of deformed category $\mathcal{O}$ and the equivariant cohomology of $ζ$-fixed locus on the affine Grassmannian attached to the Langlands dual group. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2211_03130 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | On the category $\mathcal{O}$ of a hybrid quantum group Situ, Quan Representation Theory Quantum Algebra 20G42 We study the representation theory of a hybrid quantum group at root of unity $ζ$ introduced by Gaitsgory. After discussing some basic properties of its category $\mathcal{O}$, we study deformations of the category $\mathcal{O}$. For subgeneric deformations, we construct the endomorphism algebra of big projective object and compute it explicitly. Our main result is an algebra isomorphism between the center of deformed category $\mathcal{O}$ and the equivariant cohomology of $ζ$-fixed locus on the affine Grassmannian attached to the Langlands dual group. |
| title | On the category $\mathcal{O}$ of a hybrid quantum group |
| topic | Representation Theory Quantum Algebra 20G42 |
| url | https://arxiv.org/abs/2211.03130 |