Two generalizations of the PRV conjecture

Details Two generalizations of the PRV conjecture Two generalizations of the PRV conjecture

2010-04-13

arxiv.org/abs/1004.2119v1

Mathematics

Representation Theory

Scientific paper

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.

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