Vol. 10, No. 4, 2017

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ISSN: 1944-4184 (e-only)
ISSN: 1944-4176 (print)
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
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}.

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