Two generalizations of the PRV conjecture

Abstract

Let G be a complex connected reductive group. The PRV conjecture, which was proved independently by S. Kumar and O. Mathieu in 1989, gives explicit irreducible submodules of the tensor product of two irreducible G-modules. This paper has three aims. First, we simplify the proof of the PRV conjecture, then we generalize it to other branching problems. Finally, we find other irreducible components of the tensor product of two irreducible G-modules that appear for "the same reason" as the PRV ones.

References in corpus (2)

• Geometric Invariant Theory and Generalized Eigenvalue Problem II
• Spherical homogeneous spaces of minimal rank

Cited by in corpus (3)

• Conjugation properties of tensor product multiplicities
• Additive Eigenvalue Problem (a survey), (With appendix by M. Kapovich)
• Embeddings of semisimple complex Lie groups and cohomological components of modules