# Generalized Watson Transforms II: The Complementary Series of GL(2, R)

## TL;DR

This paper constructs the complementary series representations of the group GL(2, R) using generalized Watson transforms, extending the theoretical framework for understanding these representations.

## Contribution

It introduces a novel application of generalized Watson transforms to explicitly construct the complementary series of GL(2, R).

## Key findings

- Successfully constructs the complementary series representations.
- Extends the application of Watson transforms in representation theory.
- Provides a new perspective on the structure of GL(2, R) representations.

## Abstract

\begin{abstract} We apply the theory of generalized Watson transforms developed in \cite{zheng00} to construct the complementary series of $GL(2,\R)$. \end{abstract}