On the Resolution of Reductive Monoids and Multiplicativity of $γ$-factors
In this article, we give a proof of multiplicativity for $γ$-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.
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