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Finiteness of Double Coset Spaces
Author(s) -
Lawther R.
Publication year - 1999
Publication title -
proceedings of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.899
H-Index - 65
eISSN - 1460-244X
pISSN - 0024-6115
DOI - 10.1112/s0024611599012113
Subject(s) - mathematics , coset , algebraically closed field , algebraic group , pure mathematics , class (philosophy) , character (mathematics) , reductive group , borel subgroup , variety (cybernetics) , algebraic number , permutation group , simple (philosophy) , mathematics subject classification , permutation (music) , group (periodic table) , combinatorics , algebra over a field , group theory , geometry , mathematical analysis , philosophy , chemistry , statistics , physics , organic chemistry , epistemology , artificial intelligence , computer science , acoustics
This paper makes a contribution to the classification of reductive spherical subgroups of simple algebraic groups over algebraically closed fields (a subgroup is called spherical if it has finitely many orbits on the flag variety). The author produces a class of reductive subgroups, and shows that in positive characteristic any such is spherical. The class includes all centralizers of inner involutions if the characteristic is odd, for which the result was already known thanks to work of Springer; however, the sphericality of the corresponding subgroups in even characteristic was in many cases previously undecided. The methods used are character‐theoretic in nature, and rely upon bounding inner products of permutation characters. 1991 Mathematics Subject Classification : primary 20G15; secondary 20C15.