Geometric Invariant Theory and Generalized Eigenvalue Problem II
Annales de l'Institut Fourier, Volume 61 (2011) no. 4, p. 1467-1491

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 (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 (G,G ^) as a consequence of general results on GIT-cones. We show how to read the inclusion of faces off this parametrization.

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 R (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 R (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 R (G,G ^) se lisent sur notre paramétrisation.

DOI : https://doi.org/10.5802/aif.2647
Classification:  20G05,  14L24
Keywords: Branching rule, generalized Horn problem, Littlewood-Richardson cone, GIT-cone
@article{AIF_2011__61_4_1467_0,
     author = {Ressayre, Nicolas},
     title = {Geometric Invariant Theory and Generalized Eigenvalue Problem II},
     journal = {Annales de l'Institut Fourier},
     publisher = {Association des Annales de l'institut Fourier},
     volume = {61},
     number = {4},
     year = {2011},
     pages = {1467-1491},
     doi = {10.5802/aif.2647},
     mrnumber = {2951500},
     zbl = {1245.14045},
     language = {en},
     url = {http://www.numdam.org/item/AIF_2011__61_4_1467_0}
}
Ressayre, Nicolas. Geometric Invariant Theory and Generalized Eigenvalue Problem II. Annales de l'Institut Fourier, Volume 61 (2011) no. 4, pp. 1467-1491. doi : 10.5802/aif.2647. http://www.numdam.org/item/AIF_2011__61_4_1467_0/

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