Poisson Summation and Endoscopy for SU(2,1)

TL;DR

This paper investigates the endoscopy for the group SU(2,1), providing explicit realizations of discrete series representations, trace computations, and a detailed Poisson summation formula.

Contribution

It offers new explicit realizations of discrete series, trace calculations, and a precise Poisson summation formula for SU(2,1).

Findings

Explicit realization of discrete series representations

Trace formulas for these representations

Exact Poisson summation and endoscopy formula for SU(2,1)

Abstract

In this paper we analyze the endoscopy for $SU(2,1)$. 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 Poisson summation and endoscopy for this group (in Section 4).