Poisson Summation and Endoscopy for $Sp(4,\mathbb R)$

TL;DR

This paper advances the understanding of endoscopy for the group Sp(4,R) by providing explicit realizations of discrete series, trace computations, and a detailed Poisson summation formula.

Contribution

It offers new explicit realizations of discrete series representations, trace formulas, and an exact Poisson summation formula for Sp(4,R).

Findings

Explicit realization of discrete series representations.

Trace computations for these representations.

An exact Poisson summation and endoscopy formula.

Abstract

In this paper we analyze the endoscopy for $\Sp(4,\mathbb R)$. The new results are a precise realization of the discrete series representations (in Section 2), a computation of their traces (Section 3) and an exact formula for the noncommutative Poisson summation and endoscopy of for this group (in Sections 4,5).