Modulation groups
Abstract
Conjectures of Braverman and Kazhdan, Ng\^o and Sakellaridis have motivated the development of Schwartz spaces for certain spherical varieties. We prove that under suitable assumptions these Schwartz spaces are naturally a representation of a group that we christen the modulation group. This provides a broad generalization of the defining representation of the metaplectic group. The example of a vector space and the zero locus of a quadric cone in an even number of variables are discussed in detail. In both of these cases the modulation group is closely related to algebraic groups, and we propose a conjectural method of linking modulation groups to ind-algebraic groups in general. At the end of the paper we discuss adelization and the relationship between representations of modulation groups and the Poisson summation conjecture.
Cite
@article{arxiv.2510.23932,
title = {Modulation groups},
author = {Jayce R. Getz and Armando Gutiérrez Terradillos and Farid Hosseinijafari and Bryan Hu and Seewoo Lee and Aaron Slipper and Marie-Hélène Tomé and HaoYun Yao and Alan Zhao},
journal= {arXiv preprint arXiv:2510.23932},
year = {2025}
}
Comments
Final proofreading before submission to a journal