On the Resolution of Reductive Monoids and Multiplicativity of $\gamma$-factors

TL;DR

This paper proves the multiplicativity of gamma-factors within the Braverman-Kazhdan/Ngo framework, linking it to the resolution of singularities in reductive monoids, under specific Fourier transform assumptions.

Contribution

It establishes the multiplicativity of gamma-factors assuming Fourier transform commutativity and advances the understanding of reductive monoids in the Langlands program.

Findings

Proves gamma-factor multiplicativity under certain assumptions

Analyzes the resolution of singularities in reductive monoids

Connects monoid resolution to gamma-factor properties

Abstract

In this article, we give a proof of multiplicativity for $\gamma$-factors, an equality of parabolically induced and inducing factors, in the context of the Braverman-Kazhdan/Ngo program, under the assumption of commutativity of the corresponding Fourier transforms and a certain generalized Harish-Chandra transform. We also discuss the resolution of singularities and their rationality for reductive monoids, which are among the basic objects in the program.