ON THE SOCLES OF CERTAIN PARABOLICALLY INDUCED REPRESENTATIONS OF p-ADIC CLASSICAL GROUPS

In this paper, we consider representations of p-adic classical groups parabolically induced from the products of shifted Speh representations and unitary representations of Arthur type of good parity. We describe how to compute the socles (the maximal semisimple subrepresentations) of these rep-resentations. As a consequence, we can determine whether these representa-tions are reducible or not. In particular, our results produce many unitary representations, which appear in the complementary series.

Automated summary

This paper considers representations of p-adic classical groups induced from shifted Speh representations and unitary representations of good parity Arthur type. The computation of socles allows for determining reducibility and producing many unitary representations in the complementary series.