Stable Trace Formulas and Discrete Series Representations

Details Stable Trace Formulas and Discrete Series Representations Stable Trace Formulas and Discrete Series Representations

2010-10-23

arxiv.org/abs/1010.4897v1

Mathematics

Number Theory

Scientific paper

Let G be a reductive algebraic group over Q, and suppose that Gamma is an arithmetic subgroup of G(R) defined by congruence conditions. A basic problem in arithmetic is to determine the multiplicities of discrete series representations in L^2(Gamma \ G(R)), and in general to determine the traces of Hecke operators on these spaces. In this paper we give a conjectural formula for the traces of Hecke operators, in terms of stable distributions. It is based on a stable version of Arthur's formula for L^2-Lefschetz numbers, which is due to Kottwitz. We reduce this formula to the computation of elliptic p-adic orbital integrals and the theory of endoscopic transfer. As evidence for this conjecture, we demonstrate the agreement of the central terms of this formula with the unipotent contributions to the multiplicity coming from Selberg's trace formula computed by Wakatsuki, in the case G=GSp_4 and Gamma=GSp_4(Z).

Affiliated with

Also associated with

No associations

Rating

Stable Trace Formulas and Discrete Series 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 Stable Trace Formulas and Discrete Series Representations, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Stable Trace Formulas and Discrete Series Representations will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-115992