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FINITENESS OF DOUBLE COSET SPACES

Published online by Cambridge University Press:  01 November 1999

R. LAWTHER
R. LAWTHER
Affiliation:
Department of Mathematics and Statistics, Lancaster University, Lancaster LA1 4YF, email:r.lawther@lancaster.ac.uk
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Abstract

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.

Keywords

algebraic groupsspherical subgroupspermutation characters
Type
Research Article
Information
Proceedings of the London Mathematical Society , Volume 79 , Issue 3 , November 1999 , pp. 605 - 625
Copyright
1999 London Mathematical Society

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