Towards a Littlewood Richardson rule for Kac-Moody homogeneous spaces

Pierre-Emmanuel Chaput (1, 2, 3) , Nicolas Perrin (4, 5)

1 LMJL - Laboratoire de Mathématiques Jean Leray
2 MPIM - Max Planck Institute for Mathematics
3 IECN - Institut Élie Cartan de Nancy
4 IMJ - Institut de Mathématiques de Jussieu
5 HCM - Hausdorff center of mathematics

We prove a general combinatorial formula yielding the intersection number 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 a minuscule class.

Mots clés: Schubert calculus; Kac-Moody homogeneous spaces; Littlewood-Richardson rule; jeu de taquin

Domaines: Géométrie algébrique [math.AG]

Pierre-Emmanuel Chaput, Nicolas Perrin. Towards a Littlewood Richardson rule for Kac-Moody homogeneous spaces. Journal of Lie Theory, 2012. ⟨hal-00358861⟩