Jordan decompositions in Lie algebras and their duals
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866911368600354816 |
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| author | Spice, Loren Tsai, Cheng-Chiang |
| author_facet | Spice, Loren Tsai, Cheng-Chiang |
| contents | We provide a discussion of Jordan decompositions in the Lie algebra, and the dual Lie algebra, of a reductive group in as uniform a way as possible. We give a counterexample to the claim that Jordan decompositions on the dual Lie algebra are unique, and state an upper bound on how non-unique they can be. We also prove some Chevalley-restriction-type claims about GIT quotients for the adjoint and co-adjoint actions of $G$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_07168 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Jordan decompositions in Lie algebras and their duals Spice, Loren Tsai, Cheng-Chiang Representation Theory Algebraic Geometry 22E50, 20G07, 20G15 We provide a discussion of Jordan decompositions in the Lie algebra, and the dual Lie algebra, of a reductive group in as uniform a way as possible. We give a counterexample to the claim that Jordan decompositions on the dual Lie algebra are unique, and state an upper bound on how non-unique they can be. We also prove some Chevalley-restriction-type claims about GIT quotients for the adjoint and co-adjoint actions of $G$. |
| title | Jordan decompositions in Lie algebras and their duals |
| topic | Representation Theory Algebraic Geometry 22E50, 20G07, 20G15 |
| url | https://arxiv.org/abs/2601.07168 |