Let be a connected reductive subgroup of a complex connected reductive group . Fix maximal tori and Borel subgroups of and . Consider the cone generated by the pairs of strictly dominant characters such that is a submodule of . We obtain a bijective parametrization of the faces of as a consequence of general results on GIT-cones. We show how to read the inclusion of faces off this parametrization.
Soit un sous-groupe fermé réductif et connexe d’un groupe réductif complexe et connexe . On fixe des tores maximaux et des sous-groupes de Borel de et . De cette manière les représentations irréductibles de et sont paramétrées par des poids dominants. On s’intéresse au cône engendré par les paires de poids dominants réguliers tels que est un sous--module de . Nous obtenons ici une paramétrisation bijective des faces de , en étudiant plus généralement les GIT-cônes des -variétés projectives. Nous montrons aussi comment les relations d’inclusions entre les faces de se lisent sur notre paramétrisation.
Keywords: Branching rule, generalized Horn problem, Littlewood-Richardson cone, GIT-cone
Keywords: problème de restriction, problème de Horn et ses généralisations, cône de Littlewood-Richardson, GIT- cône
Ressayre, Nicolas 1
@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}, pages = {1467--1491}, publisher = {Association des Annales de l{\textquoteright}institut Fourier}, volume = {61}, number = {4}, year = {2011}, doi = {10.5802/aif.2647}, mrnumber = {2951500}, zbl = {1245.14045}, language = {en}, url = {https://aif.centre-mersenne.org/articles/10.5802/aif.2647/} }
TY - JOUR AU - Ressayre, Nicolas TI - Geometric Invariant Theory and Generalized Eigenvalue Problem II JO - Annales de l'Institut Fourier PY - 2011 SP - 1467 EP - 1491 VL - 61 IS - 4 PB - Association des Annales de l’institut Fourier UR - https://aif.centre-mersenne.org/articles/10.5802/aif.2647/ DO - 10.5802/aif.2647 LA - en ID - AIF_2011__61_4_1467_0 ER -
%0 Journal Article %A Ressayre, Nicolas %T Geometric Invariant Theory and Generalized Eigenvalue Problem II %J Annales de l'Institut Fourier %D 2011 %P 1467-1491 %V 61 %N 4 %I Association des Annales de l’institut Fourier %U https://aif.centre-mersenne.org/articles/10.5802/aif.2647/ %R 10.5802/aif.2647 %G en %F 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. https://aif.centre-mersenne.org/articles/10.5802/aif.2647/
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