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On extended weight monoids of spherical homogeneous spaces

arxiv.org. math. Cornell University, 2020. No. 2005.05234.
Given a connected reductive complex algebraic group G and a spherical subgroup H⊂G, the extended weight monoid Λˆ+G(G/H) encodes the G-module structures on spaces of regular sections of all G-linearized line bundles on G/H. Assuming that G is semisimple and simply connected and H is specified by a regular embedding in a parabolic subgroup P⊂G, in this paper we obtain a description of Λˆ+G(G/H) via the set of simple spherical roots of~G/H together with certain combinatorial data explicitly computed from the pair (P,H). As an application, we deduce a new proof of a result of Avdeev and Gorfinkel describing Λˆ+G(G/H) in the case where H is strongly solvable.