Resumen de Strongly solvable spherical subgroups and their combinatorial invariants

Roman Avdeev

• A subgroup HH of an algebraic group GG is said to be strongly solvable if HH is contained in a Borel subgroup of GG . This paper is devoted to establishing relationships between the following three combinatorial classifications of strongly solvable spherical subgroups in reductive complex algebraic groups: Luna’s general classification of arbitrary spherical subgroups restricted to the strongly solvable case, Luna’s 1993 classification of strongly solvable wonderful subgroups, and the author’s 2011 classification of strongly solvable spherical subgroups. We give a detailed presentation of all the three classifications and exhibit interrelations between the corresponding combinatorial invariants, which enables one to pass from one of these classifications to any other.