Asymptotics of Schwartz functions

2021/12/04 by Hsu, Chun-Hsien · 1 citation
#11F55 #11F70 (Primary) #11F85 (Secondary) #FOS: Mathematics #Number Theory (math.NT) #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.2112.02403

Abstract

Let G be a split, simply connected, almost simple algebraic group, and let P be a maximal parabolic subgroup of G. Braverman and Kazhdan in \citeBKnormalized defined a Schwartz space on the affine closure X_P of P^der\backslash G. An alternate, more analytically tractable definition was given in \citeGetz:Hsu:Leslie, following several earlier works. When G is a classical group or G₂, we show the two definitions coincide and prove several previously conjectured properties of the Schwartz space that will be useful in applications. Along the way, we give an alternative construction of the ring of differential operators on X_P using the Fourier theory. We also establish the Poisson summation formulae in these cases.

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