Affine pavings of Hessenberg varieties for semisimple groups

Martha Precup*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

19 Scopus citations

Abstract

In this paper, we consider certain closed subvarieties of the flag variety, known as Hessenberg varieties. We prove that Hessenberg varieties corresponding to nilpotent elements which are regular in a Levi factor are paved by affines. We provide a partial reduction from paving Hessenberg varieties for arbitrary elements to paving those corresponding to nilpotent elements. As a consequence, we generalize results of Tymoczko asserting that Hessenberg varieties for regular nilpotent elements in the classical cases and arbitrary elements of gln(ℂ) are paved by affines. For example, our results prove that any Hessenberg variety corresponding to a regular element is paved by affines. As a corollary, in all these cases, the Hessenberg variety has no odd dimensional cohomology.

Original languageEnglish (US)
Pages (from-to)903-922
Number of pages20
JournalSelecta Mathematica, New Series
Volume19
Issue number4
DOIs
StatePublished - Nov 2013

Keywords

  • Affine paving
  • Bruhat decomposition
  • Hessenberg varieties

ASJC Scopus subject areas

  • Mathematics(all)
  • Physics and Astronomy(all)

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