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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

The Bruhat order on abelian ideals of Borel subalgebras


Authors: Jacopo Gandini, Andrea Maffei, Pierluigi Möseneder Frajria and Paolo Papi
Journal: Trans. Amer. Math. Soc. 373 (2020), 6999-7018
MSC (2010): Primary 14M17; Secondary 14M27, 17B08
DOI: https://doi.org/10.1090/tran/8092
Published electronically: July 28, 2020
MathSciNet review: 4155198
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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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Additional Information

Jacopo Gandini
Affiliation: Dipartimento di Matematica, Università di Bologna, Piazza di Porta San Donato 5, 40126 Bologna, Italy
MR Author ID: 932646
Email: jacopo.gandini@unibo.it

Andrea Maffei
Affiliation: Dipartimento di Matematica, Università di Pisa, Largo Bruno Pontecorvo 5, 56127 Pisa, Italy
MR Author ID: 612173
Email: andrea.maffei@unipi.it

Pierluigi Möseneder Frajria
Affiliation: Politecnico di Milano, Polo regionale di Como, Via Valleggio 11, 22100 Como, Italy
Email: pierluigi.moseneder@polimi.it

Paolo Papi
Affiliation: Dipartimento di Matematica, Sapienza Università di Roma, Piazzale Aldo Moro 2, 00185 Roma, Italy
MR Author ID: 322097
Email: papi@mat.uniroma1.it

Keywords: Abelian ideal, Bruhat order, nilpotent orbit, spherical variety
Received by editor(s): March 4, 2019
Received by editor(s) in revised form: November 21, 2019
Published electronically: July 28, 2020
Article copyright: © Copyright 2020 American Mathematical Society