Journal of Lie Theory 22 (2012), No. 1, 017--080
Copyright Heldermann Verlag 2012
Towards a Littlewood-Richardson Rule for Kac-Moody Homogeneous Spaces
Pierre-Emmanuel Chaput
Laboratoire de Mathématiques, UFR Sciences et Techniques, 2 rue de la Houssinière, BP 92208, 44322 Nantes Cedex 03, France
and: Max-Planck Institut Mathematik, Vivatsgasse 7, 53111 Bonn, Germany
pierre-emmanuel.chaput@math.univ-nantes.fr
Nicolas Perrin
Hausdorff Center for Mathematics, Universität Bonn, Endenicher Allee 62, 53115 Bonn, Germany
and: Institut de Mathématiques de Jussieu, Université Pierre et Marie Curie, Case 247, 4 place Jussieu, 75252 Paris Cedex 05, France
nicolas.perrin@hcm.uni-bonn.de
We prove a general combinatorial formula yielding the intersection number c(u,v,w) of three particular Λ-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.
Keywords: Littlewood-Richardson rule, Schubert calculus, Kac-Moody homogeneous spaces, jeu de taquin.
MSC: 14M15, 14N35
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