A combinatorial rule for (co)minuscule Schubert calculus

Hugh Thomas, Alexander Yong

Research output: Contribution to journalArticlepeer-review


We prove a root system uniform, concise combinatorial rule for Schubert calculus of minuscule and cominuscule flag manifolds G / P (the latter are also known as compact Hermitian symmetric spaces). We connect this geometry to the poset combinatorics of Proctor, thereby giving a generalization of Schützenberger's jeu de taquin formulation of the Littlewood-Richardson rule that computes the intersection numbers of Grassmannian Schubert varieties. Our proof introduces cominuscule recursions, a general technique to relate the numbers for different Lie types.

Original languageEnglish (US)
Pages (from-to)596-620
Number of pages25
JournalAdvances in Mathematics
Issue number2
StatePublished - Oct 1 2009


  • Algebraic combinatorics
  • Littlewood-Richardson rules
  • Minuscule Schubert varieties
  • Schubert calculus

ASJC Scopus subject areas

  • General Mathematics


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