Unitarity of Unipotent Representations of Sp(p,q) and SO*(2n)

TL;DR

This paper defines and proves the unitarity of a broad class of unipotent representations for Sp(p,q) and SO*(2n), including special cases, advancing understanding of their structure and properties.

Contribution

It introduces a comprehensive set of unipotent representations for these groups and establishes their unitarity, covering and extending previous special cases.

Findings

Unipotent representations of Sp(p,q) and SO*(2n) are unitary.

The paper confirms the unitarity of special unipotent representations.

It broadens the class of known unitary representations for these groups.

Abstract

The purpose of this paper is to define a set of representations of Sp(p,q) and SO*(2n), the unipotent representations of the title, and establish their unitarity. The unipotent representations considered here properly contain the special unipotent representations of Arthur and Barbasch-Vogan; in particular we settle the unitarity of special unipotent representations for these groups.