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2017 Equivalence classes of $\mathrm{GL}(p, \mathbb{C})\times \mathrm{GL}(q, \mathbb{C})$ orbits in the flag variety of $\mathfrak{gl}(p+q, \mathbb{C})$
Leticia Barchini, Nina Williams
Involve 10(4): 593-623 (2017). DOI: 10.2140/involve.2017.10.593

Abstract

We consider the pair of complex Lie groups

(G,K) =(GL(p + q, ),GL(p, ) × GL(q, ))

and the finite set {Q :  K-orbits on the flag variety B}. The moment map μ of the G-action on the cotangent bundle TB maps each conormal bundle closure TQB ¯ onto the closure of a single nilpotent K-orbit, OK. We use combinatorial techniques to describe μ1(OK) = {Q B : μ(TQB) = OK}.

Citation

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Leticia Barchini. Nina Williams. "Equivalence classes of $\mathrm{GL}(p, \mathbb{C})\times \mathrm{GL}(q, \mathbb{C})$ orbits in the flag variety of $\mathfrak{gl}(p+q, \mathbb{C})$." Involve 10 (4) 593 - 623, 2017. https://doi.org/10.2140/involve.2017.10.593

Information

Received: 27 September 2015; Revised: 1 March 2016; Accepted: 11 July 2016; Published: 2017
First available in Project Euclid: 12 December 2017

zbMATH: 1365.22003
MathSciNet: MR3630306
Digital Object Identifier: 10.2140/involve.2017.10.593

Subjects:
Primary: 22E47
Secondary: 22E46

Rights: Copyright © 2017 Mathematical Sciences Publishers

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