Vector bundles on quantum conjugacy classes
Fuente:
arXiv
Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2022
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866914857634234368 |
|---|---|
| author | Mudrov, Andrey |
| author_facet | Mudrov, Andrey |
| contents | 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 $t$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2201_04568 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Vector bundles on quantum conjugacy classes Mudrov, Andrey Quantum Algebra Representation Theory 17B10, 17B37, 53D55 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 $t$. |
| title | Vector bundles on quantum conjugacy classes |
| topic | Quantum Algebra Representation Theory 17B10, 17B37, 53D55 |
| url | https://arxiv.org/abs/2201.04568 |