K-orbit closures and Barbasch-Evens-Magyar varieties

Autor:	Escobar, Laura, Wyser, Benjamin J., Yong, Alexander
Rok vydání:	2017
Předmět:	Mathematics - Algebraic Geometry Mathematics - Combinatorics Mathematics - Representation Theory
Zdroj:	Pacific J. Math. 320 (2022) 103-132
Druh dokumentu:	Working Paper
DOI:	10.2140/pjm.2022.320.103
Popis:	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 $A$, 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. Comment: 22 pages, 5 figures. Accepted for publication at Pacific J. Math
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1708.06663 Zobrazit plný text záznamu View this record from Arxiv