Vector bundles on quantum conjugacy classes
| Autor: | Mudrov, Andrey |
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| Rok vydání: | 2022 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | Let $\mathfrak{g}$ be a simple complex Lie algebra of a classical type and $U_q(\mathfrak{g})$ the corresponding Drinfeld-Jimbo quantum group at $q$ not a root of unity. With every point $t$ of the fixed maximal torus $T$ of an algebraic group $G$ with Lie algebra $\mathfrak{g}$ we associate an additive category $\mathcal{O}_q(t)$ of $U_q(\mathfrak{g})$-modules that is stable under tensor product with finite-dimensional quasi-classical $U_q(\mathfrak{g})$-modules. We prove that $\mathcal{O}_q(t)$ is essentially semi-simple and use it to explicitly quantize equivariant vector bundles on the conjugacy class of $t$. Comment: 42 pages, no figures. A revised version. The main changes: a dense open set of admissible deformation parameter values is indicated |
| Databáze: | arXiv |
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