2020/05/31 by Roman Avdeev, ROMAN AVDEEV
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Algebraic group #Algebraic number #Algebraic structures and combinatorial models #Embedding #Group (periodic table) #Monoid #Reductive group #Simple (philosophy) #Simply connected space #math.AG #math.RT #msc:14M17 #msc:14M27 #msc:20G05
paper · pdf · doi:10.1007/s00031-021-09642-3
published as Transformation Groups, vol. 26 (2021), no. 2, 403-431 · v4: 27 pages, minor corrections
openalex created_date 2020/05/13 · arxiv created 2021/01/27 · openalex publication_date 2021/02/12 · arxiv updated 2021/07/14 · openalex updated_date 2026/08/05
Given a connected reductive complex algebraic group G and a spherical subgroup H ⊂ G, the extended weight monoid \widehat Λ+G(G/H) encodes the G-module structures on spaces of global 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 \widehat Λ+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 \widehat Λ+G(G/H) in the case where H is strongly solvable.