Equivalence classes of GL(p, ℂ) × GL(q, ℂ) orbits in the flag variety of 𝔤𝔩(p + q, ℂ)

Barchini, Leticia; Williams, Nina

doi:10.2140/involve.2017.10.593

Download this article
	For screen
	For printing

Recent Issues

The Journal

About the journal

Ethics and policies

Peer-review process

Submission guidelines

ISSN 1944-4184 (online)

ISSN 1944-4176 (print)

Author index

To appear

Other MSP journals

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 and Nina Williams

Vol. 10 (2017), No. 4, 593–623

DOI: 10.2140/involve.2017.10.593

Abstract

We consider the pair of complex Lie groups

(G, K) = (GL (p + q, ℂ), GL (p, ℂ) \times GL (q, ℂ))

and the finite set ${Q : K -orbits on the flag variety B}$ . The moment map $μ$ of the $G$ -action on the cotangent bundle $T^{*} B$ maps each conormal bundle closure $\bar{T_{Q}^{*} B}$ onto the closure of a single nilpotent $K$ -orbit, $O_{K}$ . We use combinatorial techniques to describe $μ^{- 1} (O_{K}) = {Q \in B : μ (T_{Q}^{*} B) = O_{K}}$ .

Keywords

nilpotent orbits, flag variety, Young tableaux

Mathematical Subject Classification 2010

Primary: 22E47

Secondary: 22E46

Milestones

Received: 27 September 2015

Revised: 1 March 2016

Accepted: 11 July 2016

Published: 7 March 2017

Communicated by Ken Ono

Authors

Leticia Barchini
Department of Mathematics Oklahoma State University Stillwater, OK 74078 United States

Nina Williams
Department of Mathematics Oklahoma State University Stillwater, OK 74078 United States

Vol. 10, No. 4, 2017