The cotangent bundle of $G/U_P$ and Kostant-Whittaker descent
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866912192889094144 |
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| author | Gannon, Tom |
| author_facet | Gannon, Tom |
| contents | We prove that the algebra of functions on the cotangent bundle $T^*(G/U_P)$ of the parabolic base affine space for a reductive group $G$ and a parabolic subgroup $P$ is isomorphic to the subalgebra of the functions on $G \times L \times \mathfrak{l}//L$ which are invariant under a certain action of the group scheme of universal centralizers on $G$, where $L$ is a Levi subgroup of $P$ and $\mathfrak{l}$ is its Lie algebra, upgrading an isomorphism of Ginzburg and Kazhdan simultaneously to the parabolic and the modular setting. We also derive a related isomorphism for the partial Whittaker cotangent bundle of $G$, which proves a conjecture of Devalapurkar. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_16844 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The cotangent bundle of $G/U_P$ and Kostant-Whittaker descent Gannon, Tom Representation Theory Algebraic Geometry We prove that the algebra of functions on the cotangent bundle $T^*(G/U_P)$ of the parabolic base affine space for a reductive group $G$ and a parabolic subgroup $P$ is isomorphic to the subalgebra of the functions on $G \times L \times \mathfrak{l}//L$ which are invariant under a certain action of the group scheme of universal centralizers on $G$, where $L$ is a Levi subgroup of $P$ and $\mathfrak{l}$ is its Lie algebra, upgrading an isomorphism of Ginzburg and Kazhdan simultaneously to the parabolic and the modular setting. We also derive a related isomorphism for the partial Whittaker cotangent bundle of $G$, which proves a conjecture of Devalapurkar. |
| title | The cotangent bundle of $G/U_P$ and Kostant-Whittaker descent |
| topic | Representation Theory Algebraic Geometry |
| url | https://arxiv.org/abs/2407.16844 |