Satellites of spherical subgroups

2016/10/24 by Victor V. Batyrev, Anne Moreau, Batyrev, Victor +1 · 1 citation
Mathematics · #14L30 #14M27 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #FOS: Mathematics #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.1610.07377

openalex publication_date 2016/10/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let G be a complex connected reductive algebraic group. Given a spherical subgroup H ⊂ G and a subset I of the set of spherical roots of G/H, we define, up to conjugation, a spherical subgroup H_I ⊂ G of the same dimension of H, called a satellite. We investigate various interpretations of the satellites. We also show a close relation between the Poincaré polynomials of the two spherical homogeneous spaces G/H and G/H_I.

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