Harmonic analysis on spherical homogeneous spaces with solvable stabilizer

TL;DR

This paper computes the spectra of group representations on line bundle sections over spherical homogeneous spaces with solvable stabilizers, extending harmonic analysis in algebraic geometry.

Contribution

It provides explicit spectral computations for G/H where G is semisimple and H is solvable, a novel case in harmonic analysis on spherical spaces.

Findings

Spectra of representations are explicitly computed.

Results apply to all spherical homogeneous spaces with solvable stabilizers.

Advances understanding of harmonic analysis on these spaces.

Abstract

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.