Generalization of a theorem of Waldspurger to nice representations

Details Generalization of a theorem of Waldspurger to nice representations Generalization of a theorem of Waldspurger to nice representations

2001-06-28

arxiv.org/abs/math/0106245v1

Mathematics

Algebraic Geometry

38 pages, AMSLatex

Scientific paper

A theorem of Waldspurger states that the Fourier transform of a stable distribution on the Lie algebra of a simply-connected semisimple group $G$ over a p-adic field, is again stable. We generalize this theorem to representations whose generic stabilizer subgroup is connected and reductive (assuming that $G$ is simple). In this more general situation the Fourier transform of a stable distribution is stable up to a sign that we describe explicitly. The proof is based on the $p$-adic stationary phase principle and on the global techniques introduced by Kottwitz for stabilization of the trace formula. As an application of our main theorem, we find the explicit diagonalization of the gamma-matrix for the prehomogeneous space of symmetric $n\times n$ matrices over a p-adic field (for odd $n$).

Affiliated with

Also associated with

No associations

Rating

Generalization of a theorem of Waldspurger to nice representations does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Generalization of a theorem of Waldspurger to nice representations, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Generalization of a theorem of Waldspurger to nice representations will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-124662