no. 4
Geometric Invariant Theory and Generalized Eigenvalue Problem II
Ressayre, Nicolas1
1 Université Montpellier II Département de Mathématiques Case courrier 051 - Place Eugène Bataillon 34095 Montpellier Cedex 5 (France)
Annales de l'Institut Fourier, Tome 61 (2011) no. 4, pp. 1467-1491.

Soit G un sous-groupe fermé réductif et connexe d’un groupe réductif complexe et connexe G ^. On fixe des tores maximaux et des sous-groupes de Borel de G et G ^. De cette manière les représentations irréductibles de G et G ^ sont paramétrées par des poids dominants. On s’intéresse au cône ℒR ∘ (G,G ^) engendré par les paires (ν,ν ^) de poids dominants réguliers tels que V ν * est un sous-G-module de V ν ^ . Nous obtenons ici une paramétrisation bijective des faces de ℒR ∘ (G,G ^), en étudiant plus généralement les GIT-cônes des G-variétés projectives. Nous montrons aussi comment les relations d’inclusions entre les faces de ℒR ∘ (G,G ^) se lisent sur notre paramétrisation.

Let G be a connected reductive subgroup of a complex connected reductive group G ^. Fix maximal tori and Borel subgroups of G and G ^. Consider the cone ℒℛ ∘ (G,G ^) generated by the pairs (ν,ν ^) of strictly dominant characters such that V ν * is a submodule of V ν ^ . We obtain a bijective parametrization of the faces of ℒℛ ∘ (G,G ^) as a consequence of general results on GIT-cones. We show how to read the inclusion of faces off this parametrization.

DOI : 10.5802/aif.2647
Classification : 20G05, 14L24
Keywords: Branching rule, generalized Horn problem, Littlewood-Richardson cone, GIT-cone
Mots clés : problème de restriction, problème de Horn et ses généralisations, cône de Littlewood-Richardson, GIT- cône
Ressayre, Nicolas 1

1 Université Montpellier II Département de Mathématiques Case courrier 051 - Place Eugène Bataillon 34095 Montpellier Cedex 5 (France) 
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Ressayre, Nicolas. Geometric Invariant Theory and Generalized Eigenvalue Problem II. Annales de l'Institut Fourier, Tome 61 (2011) no. 4, pp. 1467-1491. doi : 10.5802/aif.2647. http://www.numdam.org/articles/10.5802/aif.2647/

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