Coxeter Combinatorics and Spherical Schubert Geometry

Reuven Hodges, Alexander Yong

Research output: Contribution to journalArticlepeer-review


For a finite Coxeter system and a subset of its diagram nodes, we define spherical elements (a generalization of Coxeter elements). Conjecturally, for Weyl groups, spherical elements index Schubert varieties in a flag manifold G/B that are spherical for the action of a Levi subgroup. We evidence the conjecture, employing the combinatorics of Demazure modules, and work of R. Avdeev and A. Petukhov, M. Can and R. Hodges, R. Hodges and V. Lakshmibai, P. Karuppuchamy, P. Magyar and J. Weyman and A. Zelevinsky, N. Perrin, J. Stembridge, and B. Tenner. In type A, we establish connections with the key polynomials of A. Lascoux and M.P. Schützenberger, multiplicity-freeness, and split-symmetry in algebraic combinatorics. Thereby, we invoke theorems of A. Kohnert, V. Reiner and M. Shimozono, and C. Ross and A. Yong.

Original languageEnglish (US)
Pages (from-to)447-474
Number of pages28
JournalJournal of Lie Theory
Issue number2
StatePublished - 2022


  • Schubert varieties
  • key polynomials
  • spherical varieties
  • split symmetry

ASJC Scopus subject areas

  • Algebra and Number Theory


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