Kazhdan-lusztig polynomials and drift configurations

Research output: Contribution to journalArticle

Abstract

The coefficients of the Kazhdan-Lusztig polynomials Pv;w.q/ are nonnegative integers that are upper semicontinuous relative to Bruhat order. Conjecturally, the same properties hold for h-polynomials Hv;w.q/ of local rings of Schubert varieties. This suggests a parallel between the two families of polynomials. We prove our conjectures for Grassmannians, and more generally, covexillary Schubert varieties in complete flag varieties, by deriving a combinatorial formula for Hv;w.q/. We introduce drift configurations to formulate a new and compatible combinatorial rule for Pv;w.q/. From our rules we deduce, for these cases, the coefficient-wise inequality Pv;w.q/≤Hv;w.q/.

Original languageEnglish (US)
Pages (from-to)594-623
Number of pages30
JournalAlgebra and Number Theory
Volume5
Issue number5
DOIs
StatePublished - 2011

Keywords

  • Hilbert series
  • Kazhdan-lusztig polynomials
  • Schubert varieties

ASJC Scopus subject areas

  • Algebra and Number Theory

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