Generic states and stability
| Autor: | Hyeon, Donghoon, Park, Junyoung |
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| Rok vydání: | 2017 |
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| Druh dokumentu: | Working Paper |
| Popis: | We define the notion of the generic state polytope, analogous to the generic initial ideal and prove its existence: This greatly generalizes the work of R\"omer and Schmitz who proved the existence of generic Gr\"ober fans. We also show that a generic state polytope always contains the trivial character: Equivalently, in any GIT quotient problem of semisimple group representations, every point is semistable with respect to a {\it general} maximal torus. Also, we revisit Kempf's proof of the existence of the worst one parameter subgroup (1-ps) and describe the equations for determining the worst 1-ps. Comment: 13 pages |
| Databáze: | arXiv |
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