K-ORBIT CLOSURES AND BARBASCH–EVENS–MAGYAR VARIETIES

Laura Escobar, Benjamin J. Wyser, Alexander Yong

Research output: Contribution to journalArticlepeer-review

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 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.

Original languageEnglish (US)
Pages (from-to)103-132
Number of pages30
JournalPacific Journal of Mathematics
Volume320
Issue number1
DOIs
StatePublished - 2022

Keywords

  • Barbasch–evens–magyar variety
  • Clans
  • Flag variety
  • K-orbit
  • Moment polytope

ASJC Scopus subject areas

  • Mathematics(all)

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