A remark on the simple cuspidal representations of GL(n, F)

2013/10/13 by Peng Xu, Xu, Peng · 1 citation
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #FOS: Mathematics #Finite Group Theory Research #Number Theory (math.NT) #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.1310.3519

openalex publication_date 2013/10/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let F be a non-archimedean local field of residue characteristic p, G be the group GL(n, F). In this note, under the assumption (n, p)=1, we show a simple cuspidal representation π (that with normalized level (1)/(n)) of G is determined uniquely up to isomorphism by the local constants of χ∘ det⊗ π for all characters χ of F^×.

Citations

• The Local Langlands Correspondence for Simple Supercuspidal Representations of GL_n(F)

Cited by

• On the Local Converse Theorem for Depth (1)/(N) Supercuspidal Representations of GL(2N, F)

Related

• Cuspidal representations of GL(n,F) distinguished by a maximal Levi subgroup, with F a non-archimedean local field
• Cuspidal ℓ-modular representations of GL_n(F) distinguished by a Galois involution
• Generic cuspidal representations of U(2,1)
• Représentations cuspidales de GL(r,D) distinguées par une involution intérieure
• Characterisation of the poles of the ℓ-modular Asai L-factor