C*-algebraic normalization and Godement-Jacquet factors

TL;DR

This paper explores the connection between distributional methods on GL(n) that produce Godement-Jacquet gamma factors and their natural emergence in the C*-algebraic normalization of standard intertwining integrals on SL(n+1).

Contribution

It reveals a natural appearance of Godement-Jacquet gamma factors within the C*-algebraic normalization framework for intertwining operators.

Findings

Distribution on GL(n) generates Godement-Jacquet gamma factors

Gamma factors appear naturally in C*-algebraic normalization

Links between harmonic analysis and operator algebras in representation theory

Abstract

We observe how certain distribution on $\mathrm{GL}(n)$ that generates Godement-Jacquet $\gamma$-factors appears naturally in the C*-algebraic normalization process for standard intertwining integrals on $\mathrm{SL}(n+1)$.