Multiplicity One for Unitary Ginzburg--Rallis Models over Local Fields

Yuxuan Ge; Sagnik Mukherjee; Junyi Zhai

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arXiv · 2610.36294

Multiplicity One for Unitary Ginzburg--Rallis Models over Local Fields

Yuxuan Ge·Sagnik Mukherjee·Junyi Zhai

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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.

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BibTeX RIS

Yuxuan Ge, Sagnik Mukherjee, Junyi Zhai. 2026-10-26. Multiplicity One for Unitary Ginzburg--Rallis Models over Local Fields. https://arxiv.org/abs/2610.36294

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