Poisson Summation and Endoscopy for $SL(3,\mathbb{R})$

The group is interesting as the first example of split rank 2 semisimple group, all the irreducible unitary representations of which are known. We make a precise realization of the discrete series representations (in Section 2) by using the Orbit Method and Geometric Quantization, a computation of their traces (Section 3) and an exact formula for the noncommutative Poisson summation and endoscopy of for this group (in Section 4).