Year: 2026
Type: preprint
Abstract: Let $F$ be a non-Archimedean local field of characteristic zero. We prove multiplicity one for every irreducible smooth admissible representation in the split forms of Wan-Zhang Models 6-10. Combining the Gelfand-Kazhdan method with nilpotent-wavefront restrictions on Bernstein-finite equivariant distributions, we establish the required symmetries through rational orbit analysis, parabolic descent, stabilizer characters, and conormal arguments. The type-$D_6$ analysis treats both the vector-similitude group of Model 9 and the semispin form arising in the exceptional $E_7$ model. For Model 10, the distribution theorem gives a product bound for periods; the individual multiplicity bound follows from Langlands classification and a vanishing theorem for standard modules induced from nongeneric tempered data on the maximal $E_6$ Levi.
Source: arXiv (Cornell University)
Author: Ge, Yuxuan
Language: English
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7221803442