|
|||||
|
|
|
|
|
|
|
|
|
|
|
|
|
${\sf K}$-orbit
closures and Barbasch–Evens–Magyar varieties
Laura Escobar, Benjamin J. Wyser and Alexander Yong |
|
Vol. 320 (2022), No. 1, 103–132
|
Abstract |
|
We define the Barbasch–Evens–Magyar varieties. We show they are isomorphic to the smooth varieties defined in [D. Barbasch and S. Evens 1994] that map generically finitely to symmetric orbit closures, thereby giving resolutions of singularities in certain cases. Our definition parallels P. Magyar’s [1998] construction of the Bott–Samelson varieties [H. C. Hansen 1973; M. Demazure 1974]. From this alternative viewpoint, one deduces a graphical description in type , stratification into closed subvarieties of the same kind, and determination of the torus-fixed points. Moreover, we explain how these manifolds inherit a natural symplectic structure with Hamiltonian torus action. We then express the moment polytope in terms of the moment polytope of a Bott–Samelson variety. |
PDF Access Denied
We have not been able to recognize your IP address
3.145.188.160
as that of a subscriber to this journal.
Online access to the content of recent issues is by
subscription, or purchase of single articles.
Please contact your institution's librarian suggesting a subscription, for example by using our journal-recommendation form. Or, visit our subscription page for instructions on purchasing a subscription.
You may also contact us at
contact@msp.org
or by using our
contact form.
Or, you may purchase this single article for USD 40.00:
Keywords
flag variety, $\sf{K}$-orbit, Barbasch–Evens–Magyar
variety, moment polytope, clans
|
Mathematical Subject Classification
Primary: 14M15
|
Milestones
Received: 27 August 2020
Revised: 4 July 2022
Accepted: 16 July 2022
Published: 16 October 2022
|
Authors |
| Laura Escobar | |
| Department of Mathematics and
Statistics Washington University in St. Louis St. Louis, MO United States |
|
| Benjamin J. Wyser | |
| Elkridge, MD United States |
|
| Alexander Yong | |
| Department of Mathematics University of Illinois at Urbana-Champaign Urbana, IL United States |
|
