K-orbit closures and Barbasch-Evens-Magyar varieties
Abstract
We define the Barbasch-Evens-Magyar varieties. We show they are isomorphic to the smooth varieties defined in [D.~Barbasch-S.~Evens '94] that map generically finitely to symmetric orbit closures, thereby giving resolutions of singularities in certain cases. Our definition parallels [P.~Magyar '98]'s construction of the Bott-Samelson varieties [H.~C.~Hansen '73, M.~Demazure '74]. 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.
Cite
@article{arxiv.1708.06663,
title = {K-orbit closures and Barbasch-Evens-Magyar varieties},
author = {Laura Escobar and Benjamin J. Wyser and Alexander Yong},
journal= {arXiv preprint arXiv:1708.06663},
year = {2022}
}
Comments
22 pages, 5 figures. Accepted for publication at Pacific J. Math