2022/05/29 by Itay Naor, Naor, Itay
Mathematics · #20C33 #20G05 (Primary) 46F10 #22E50 #22E50 (Secondary) #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #FOS: Mathematics #Finite Group Theory Research #Representation Theory (math.RT)
paper · pdf · doi:10.48550/arxiv.2205.15313
openalex publication_date 2022/05/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We define a generalization of Shalika models for GLn+m(F) and prove that they are multiplicity-free, where F is either a non-Archimedean local field or a finite field and n,m are any natural numbers. In particular, we give new proof for the case of n=m. We also show that the Bernstein-Zelevinsky product of an irreducible representation of GLn(F) and the trivial representation of GLm(F) is multiplicity-free. We relate the two results by a conjecture about twisted parabolic induction of Gelfand pairs.