# On the analytic properties of intertwining operators II: local degree bounds and limit multiplicities

## TL;DR

This paper investigates the analytic properties of intertwining operators for reductive groups over p-adic fields, providing bounds and applications to limit multiplicity problems in number theory.

## Contribution

It extends previous work by analyzing local degree bounds of matrix coefficients, enabling control over global intertwining operators for various reductive groups.

## Key findings

- Controlled the degrees of matrix coefficients of intertwining operators.
- Established bounds for global normalizing factors.
- Applied results to the limit multiplicity problem.

## Abstract

In this paper we continue to study the degrees of matrix coefficients of intertwining operators associated to reductive groups over $p$-adic local fields. Together with previous analysis of global normalizing factors we can control the analytic properties of global intertwining operators for a large class of reductive groups over number fields, in particular for inner forms of $GL(n)$ and $SL(n)$ and quasi-split classical groups. This has a direct application to the limit multiplicity problem for these groups.