Two generalizations of the PRV conjecture

Pierre-Louis Montagard (1) , Boris Pasquier (1) , Nicolas Ressayre (1)

1 I3M - Institut de Mathématiques et de Modélisation de Montpellier

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.

Domaines: Théorie des représentations [math.RT]; Géométrie algébrique [math.AG]

Pierre-Louis Montagard, Boris Pasquier, Nicolas Ressayre. Two generalizations of the PRV conjecture. Compositio Mathematica, 2011, 147 (04), pp.1321-1336. ⟨10.1112/S0010437X10005233⟩. ⟨hal-00471690⟩