Cohomology of Iwasawa subgroup of the group $U(p,p)$ in nonunitary representations

TL;DR

This paper investigates the cohomology of a specific Iwasawa subgroup within the group U(p,p) through nonunitary representations, exploring the existence of unitary representations with similar properties for p>2.

Contribution

It introduces a special nonunitary representation of the Iwasawa subgroup with nontrivial cohomology and suggests the potential for unitary representations with this property when p>2.

Findings

Existence of nonunitary representations with nontrivial cohomology.

Potential for unitary representations with similar properties for p>2.

Abstract

We consider special nonuntary represenation of the Iwasawa subgrouh with a nontrivial cohomology. For $p>2$ presunabley there are unitary representations with this property.