Geometric Invariant Theory and Generalized Eigenvalue Problem II

Nicolas Ressayre[1]

  • [1] Université Montpellier II Département de Mathématiques Case courrier 051 - Place Eugène Bataillon 34095 Montpellier Cedex 5 (France)

Annales de l’institut Fourier (2011)

  • Volume: 61, Issue: 4, page 1467-1491
  • ISSN: 0373-0956

Abstract

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

How to cite

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Ressayre, Nicolas. "Geometric Invariant Theory and Generalized Eigenvalue Problem II." Annales de l’institut Fourier 61.4 (2011): 1467-1491. <http://eudml.org/doc/219780>.

@article{Ressayre2011,
abstract = {Let $G$ be a connected reductive subgroup of a complex connected reductive group $\hat\{G\}$. Fix maximal tori and Borel subgroups of $G$ and $\hat\{G\}$. Consider the cone $\mathcal\{L\}\mathcal\{R\}^\circ (G,\hat\{G\})$ generated by the pairs $(\nu ,\hat\{\nu \})$ of strictly dominant characters such that $V_\nu ^*$ is a submodule of $V_\{\hat\{\nu \}\}$. We obtain a bijective parametrization of the faces of $\mathcal\{L\}\mathcal\{R\}^\circ (G,\hat\{G\})$ as a consequence of general results on GIT-cones. We show how to read the inclusion of faces off this parametrization.},
affiliation = {Université Montpellier II Département de Mathématiques Case courrier 051 - Place Eugène Bataillon 34095 Montpellier Cedex 5 (France)},
author = {Ressayre, Nicolas},
journal = {Annales de l’institut Fourier},
keywords = {Branching rule; generalized Horn problem; Littlewood-Richardson cone; GIT-cone; branching rule},
language = {eng},
number = {4},
pages = {1467-1491},
publisher = {Association des Annales de l’institut Fourier},
title = {Geometric Invariant Theory and Generalized Eigenvalue Problem II},
url = {http://eudml.org/doc/219780},
volume = {61},
year = {2011},
}

TY - JOUR
AU - Ressayre, Nicolas
TI - Geometric Invariant Theory and Generalized Eigenvalue Problem II
JO - Annales de l’institut Fourier
PY - 2011
PB - Association des Annales de l’institut Fourier
VL - 61
IS - 4
SP - 1467
EP - 1491
AB - Let $G$ be a connected reductive subgroup of a complex connected reductive group $\hat{G}$. Fix maximal tori and Borel subgroups of $G$ and $\hat{G}$. Consider the cone $\mathcal{L}\mathcal{R}^\circ (G,\hat{G})$ generated by the pairs $(\nu ,\hat{\nu })$ of strictly dominant characters such that $V_\nu ^*$ is a submodule of $V_{\hat{\nu }}$. We obtain a bijective parametrization of the faces of $\mathcal{L}\mathcal{R}^\circ (G,\hat{G})$ as a consequence of general results on GIT-cones. We show how to read the inclusion of faces off this parametrization.
LA - eng
KW - Branching rule; generalized Horn problem; Littlewood-Richardson cone; GIT-cone; branching rule
UR - http://eudml.org/doc/219780
ER -

References

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  15. N. Ressayre, Geometric Invariant Theory and Generalized Eigenvalue Problem, Invent. Math. 180 (2010), 389-441 Zbl1197.14051MR2609246
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