Proper elements of Coxeter groups

József Balogh, David Brewster, Reuven Hodges

Research output: Contribution to journalArticlepeer-review

Abstract

We extend the notion of proper elements to all finite Coxeter groups. For all infinite families of finite Coxeter groups we prove that the probability a random element is proper goes to zero in the limit. This proves a conjecture of the third author and Alexander Yong regarding the proportion of Schubert varieties that are Levi spherical for all infinite families of Weyl groups. We also enumerate the proper elements in the exceptional Coxeter groups.

Original languageEnglish (US)
Article number32
JournalEuropean Journal of Mathematics
Volume10
Issue number2
DOIs
StatePublished - Jun 2024

Keywords

  • 05E14
  • 14M15
  • 20P05
  • Chernoff bounds
  • Proper elements
  • Schubert varieties
  • Spherical varieties

ASJC Scopus subject areas

  • General Mathematics

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