Stein--Sahi complementary series and their degenerations

TL;DR

This paper introduces Stein--Sahi complementary series, holomorphic series, and unipotent representations for U(n,n), discussing their properties and open problems in the context of representation theory.

Contribution

It provides an accessible introduction to these series and representations, highlighting open problems and focusing on the group U(n,n).

Findings

Introduction of Stein--Sahi complementary series and holomorphic series

Discussion of unipotent representations for U(n,n)

Identification of open problems in the area

Abstract

The aim of the paper is an introduction to Stein--Sahi complementary series, holomorphic series, and 'unipotent representations'. We also discuss some open problems related to these objects. For the sake of simplicity, we consider only the groups U(n,n).