Satellites of spherical subgroups

Victor Batyrev; Anne Moreau

Satellites of spherical subgroups

Algebraic Geometry 2019-01-01 v2 Representation Theory

Authors: Victor Batyrev , Anne Moreau

Abstract

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

Keywords

nilpotent orbits

Cite

@article{arxiv.1610.07377,
  title  = {Satellites of spherical subgroups},
  author = {Victor Batyrev and Anne Moreau},
  journal= {arXiv preprint arXiv:1610.07377},
  year   = {2019}
}

Comments

27 pages in English. Several minor changes and significantly improved exhibition. Main results unchanged. Accepted for publication in Algebraic Geometry journal

Satellites of spherical subgroups

Abstract

Keywords

Cite

Comments

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