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. 
Roman Avdeev and Natalia Gorfinkel
math.RT math.AG