Extended weight semigroups of affine spherical homogeneous spaces of non-simple semisimple algebraic groups

Abstract

The extended weight semigroup of a homogeneous space G/H of a connected semisimple algebraic group G characterizes the spectra of the representations of G on the spaces of regular sections of homogeneous linear bundles over G/H, including the space of regular functions on G/H. We compute the extended weight semigroups for all strictly irreducible affine spherical homogeneous spaces G/H, where G is a simply connected non-simple semisimple complex algebraic group and H a connected closed subgroup of it. In all the cases we also find the highest weight functions corresponding to the indecomposable elements of this semigroup. Among other things, our results complete the computation of the weight semigroups for all strictly irreducible simply connected affine spherical homogeneous spaces of semisimple complex algebraic groups.

v2: 23 pages, cosmetic changes

Cited by in corpus (5)

• Restricted Roots and Restricted Form of Weyl Dimension Formula for Spherical Varieties
• Affine spherical homogeneous spaces with good quotient by a maximal unipotent subgroup
• On the extended weight monoid and its applications to orthogonal polynomials
• Degenerations of spherical subalgebras and spherical roots
• On some families of smooth affine spherical varieties of full rank