2020/10/30 by Dor Mezer, Mezer, Dor
Mathematics · #20G25 #22E50 (Primary) 20G05 #46F10 (Secondary) #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #FOS: Mathematics #Finite Group Theory Research #Representation Theory (math.RT)
paper · doi:10.48550/arxiv.2010.16112
openalex publication_date 2020/10/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In [AGRS] a multiplicity one theorem is proven for general linear groups, orthogonal groups and unitary groups (GL, O, and U) over p-adic local fields. That is to say that when we have a pair of such groups Gn⊆ Gn+1, any restriction of an irreducible smooth representation of Gn+1 to Gn is multiplicity free. This property is already known for GL over a local field of positive characteristic, and in this paper we also give a proof for O,U, and SO over local fields of positive odd characteristic. These theorems are shown in [GGP] to imply the uniqueness of Bessel models, and in [CS] to imply the uniqueness of Rankin-Selberg models. We also prove simultaniously the uniqeuness of Fourier-Jacobi models, following the outlines of the proof in [Sun]. By the Gelfand-Kazhdan criterion, the multiplicity one property for a pair H≤ G follows from the statement that any distribution on G invariant to conjugations by H is also invariant to some anti-involution of G preserving H.