Gan-Gross-Prasad Conjecture for U(p,q)

TL;DR

This paper proves the Gan-Gross-Prasad conjecture for discrete series representations of U(p,q), characterizing when certain subrepresentations occur upon restriction based on interlacing parameters.

Contribution

It provides a proof of the conjecture specifically for discrete series of U(p,q), clarifying the interlacing conditions for subrepresentation inclusion.

Findings

Established the interlacing condition for discrete series restrictions

Confirmed the conjecture for U(p,q) discrete series

Characterized subrepresentation occurrence via Harish-Chandra parameters

Abstract

In this paper, we give a proof of the Gan-Gross-Prasad conjecture for the discrete series of U(p,q). Given a discrete series representation $D(\lambda)$ in terms of the Harish-Chandra parameter, the restriction of $D(\lambda)$ to U(p-1,q) contains $D(\mu)$ as a subrepresentation if and only if $\lambda$ and $\mu$ interlaces in a very special way.