Year: 2026
Type: preprint
Abstract: We prove multiplicity at most one for the unitary similitude Ginzburg--Rallis model over local fields of characteristic zero, for both the quasi-split and non-quasi-split groups. The theorem holds for all irreducible smooth representations over non-Archimedean fields and all irreducible Casselman--Wallach representations over the real field. We first describe the decomposition into parabolic double cosets and compute the required stabilizers. Over a non-Archimedean field we use character obstructions, localization, and transpose symmetry. Over the real field we use a Casimir identity and explicit normal vectors to prove the corresponding statement for distributions with prescribed infinitesimal character. The Gelfand--Kazhdan criterion and a dualizing involution then give the multiplicity bound.
Source: arXiv (Cornell University)
Authors: Ge, Yuxuan, Mukherjee, Sagnik, Zhai, Junyi
Language: English
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7224135874