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- W4287904800 abstract "Let $G$ be a reductive algebraic group and let $Z$ be the stabilizer of a nilpotent element $e$ of the Lie algebra of $G$. We consider the action of $Z$ on the flag variety of $G$, and we focus on the case where this action has a finite number of orbits (i.e., $Z$ is a spherical subgroup). This holds for instance if $e$ has height $2$. In this case we give a parametrization of the $Z$-orbits and we show that each $Z$-orbit has a structure of algebraic affine bundle. In particular, in type $A$, we deduce that each orbit has a natural cell decomposition. In the aim to study the (strong) Bruhat order of the orbits, we define an abstract partial order on certain quotients associated to a Coxeter system. In type $A$, we show that the Bruhat order of the $Z$-orbits can be described in this way." @default.
- W4287904800 created "2022-07-26" @default.
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- W4287904800 date "2020-01-13" @default.
- W4287904800 modified "2023-10-18" @default.
- W4287904800 title "Parametrization, structure and Bruhat order of certain spherical quotients" @default.
- W4287904800 doi "https://doi.org/10.48550/arxiv.2001.04411" @default.
- W4287904800 hasPublicationYear "2020" @default.
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