26,397 research outputs found
Gindikin-Karpelevich finiteness for Kac-Moody groups over local fields
In this paper, we prove some finiteness results about split Kac-Moody groups
over local non-archimedean fields. Our results generalize those of "An affine
Gindikin-Karpelevich formula" by Alexander Braverman, Howard Garland, David
Kazhdan and Manish Patnaik. We do not require our groups to be affine. We use
the hovel I associated to this situation, which is the analogue of the
Bruhat-Tits building for a reductive group.Comment: International Mathematics Research Notices, Oxford University Press
(OUP), 201
Convexity in a masure
Masures are generalizations of Bruhat-Tits buildings. They were introduced to
study Kac-Moody groups over ultrametric fields, which generalize reductive
groups over the same fields. If A and A are two apartments in a building, their
intersection is convex (as a subset of the finite dimensional affine space A)
and there exists an isomorphism from A to A fixing this intersection. We study
this question for masures and prove that the analogous statement is true in
some particular cases. We deduce a new axiomatic of masures, simpler than the
one given by Rousseau
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