The Bruhat order on abelian ideals of Borel subalgebras

Gandini, Jacopo; Maffei, Andrea; Möseneder Frajria, Pierluigi; Papi, Paolo

doi:10.1090/tran/8092

The Bruhat order on abelian ideals of Borel subalgebras
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by Jacopo Gandini, Andrea Maffei, Pierluigi Möseneder Frajria and Paolo Papi PDF

Trans. Amer. Math. Soc. 373 (2020), 6999-7018 Request permission

Abstract:

Let $G$ be a quasi-simple algebraic group over an algebraically closed field $\mathsf {k}$ whose characteristic is not very bad for $G$, and let $B$ be a Borel subgroup of $G$ with Lie algebra $\mathfrak {b}$. Given a $B$-stable abelian subalgebra $\mathfrak {a}$ of the nilradical of $\mathfrak {b}$, we parametrize the $B$-orbits in $\mathfrak {a}$ and we describe their closure relations.

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