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arXiv · 1110.4621

Generalizations of the PRV conjecture, II

Pierre-Louis Montagard·Boris Pasquier·Nicolas Ressayre
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Abstract

Let $G\subset\hat{G}$ be two complex connected reductive groups. We deals with the hard problem of finding sub-$G$-modules of a given irreducible $\hat{G}$-module. In the case where $G$ is diagonally embedded in $\hat{G}=G\times G$, S. Kumar and O. Mathieu found some of them, proving the PRV conjecture. Recently, the authors generalized the PRV conjecture on the one hand to the case where $\hat{G}/G$ is spherical of minimal rank, and on the other hand giving more sub-$G$-modules in the classical case $G\subset G\times G$. In this paper, these two recent generalizations are combined in a same more general result.

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Pierre-Louis Montagard, Boris Pasquier, Nicolas Ressayre. 2011-10-20. Generalizations of the PRV conjecture, II. https://arxiv.org/abs/1110.4621

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