773 research outputs found
Infiniteness of Double Coset Collections in Algebraic Groups
Let be a linear algebraic group defined over an algebraically closed
field. The double coset question addressed in this paper is the following:
Given closed subgroups and , is the double coset collection finite or infinite? We limit ourselves to the case where is maximal
rank and reductive and parabolic. This paper presents a criterion for
infiniteness which involves only dimensions of centralizers of semisimple
elements. This result is then applied to finish the classification of those
which are spherical. Finally, excluding a case in , we show that if
is finite then is spherical or the Levi factor of is
spherical. This implies that it is rare for to be finite. The
primary method of proof is to descend to calculations at the finite group level
and then to use elementary character theory.Comment: 24 page
Classification of double flag varieties of complexity 0 and 1
A classification of double flag varieties of complexity 0 and 1 is obtained.
An application of this problem to decomposing tensor products of irreducible
representations of semisimple Lie groups is considered
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