3 research outputs found
Two generalizations of the PRV conjecture
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
Harmonic analysis on spherical homogeneous spaces with solvable stabilizer
For all spherical homogeneous spaces G/H, where G is a simply connected
semisimple algebraic group and H a connected solvable subgroup of G, we compute
the spectra of the representations of G on spaces of regular sections of
homogeneous line bundles over G/H.Comment: v2: 14 pages, minor correction