Towards a Littlewood-Richardson rule for Kac-Moody homogeneous spaces

Abstract

We prove a general combinatorial formula yielding the intersection number $c_{u,v}^w$ of three particular $\Lambda$-minuscule Schubert classes in any Kac-Moody homogeneous space, generalising the Littlewood-Richardson rule. The combinatorics are based on jeu de taquin rectification in a poset defined by the heap of $w$.

arXiv comment50 pages, option showlabels removed

References in corpus (2)

• d-Complete Posets Generalize Young Diagrams for the Jeu de Taquin Property
• A combinatorial rule for (co)minuscule Schubert calculus

Cited by in corpus (3)

• Unique rectification in $d$-complete posets: towards the $K$-theory of Kac-Moody flag varieties
• On the big quantum cohomology of coadjoint varieties
• Root-theoretic Young diagrams and Schubert calculus: planarity and the adjoint varieties