Journal of Lie Theory

no. 1
Towards a Littlewood-Richardson Rule for Kac-Moody Homogeneous Spaces
Pierre-Emmanuel Chaput1, 2; Nicolas Perrin3, 4
1Laboratoire de Mathématiques, UFR Sciences et Techniques, 2 rue de la Houssinière, BP 92208, 44322 Nantes Cedex 03, France
2Max-Planck Institut Mathematik, Vivatsgasse 7, 53111 Bonn, Germany
3Hausdorff Center for Mathematics, Universität Bonn, Endenicher Allee 62, 53115 Bonn, Germany
4Institut de Mathématiques de Jussieu, Université Pierre et Marie Curie, Case 247, 4 place Jussieu, 75252 Paris Cedex 05, France
Journal of Lie Theory, Volume 22 (2012) no. 1, pp. 17-80
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.
DOI: 10.5802/jolt.660
Classification: 14M15, 14N35
Keywords: Littlewood-Richardson rule, Schubert calculus, Kac-Moody homogeneous spaces, jeu de taquin

Pierre-Emmanuel Chaput  1 , 2 ; Nicolas Perrin  3 , 4

1 Laboratoire de Mathématiques, UFR Sciences et Techniques, 2 rue de la Houssinière, BP 92208, 44322 Nantes Cedex 03, France
2 Max-Planck Institut Mathematik, Vivatsgasse 7, 53111 Bonn, Germany
3 Hausdorff Center for Mathematics, Universität Bonn, Endenicher Allee 62, 53115 Bonn, Germany
4 Institut de Mathématiques de Jussieu, Université Pierre et Marie Curie, Case 247, 4 place Jussieu, 75252 Paris Cedex 05, France 
Pierre-Emmanuel Chaput; Nicolas Perrin. Towards a Littlewood-Richardson Rule for Kac-Moody Homogeneous Spaces. Journal of Lie Theory, Volume 22 (2012) no. 1, pp. 17-80. doi: 10.5802/jolt.660
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