A mod-p metaplectic Montréal functor

2022/08/26 by Robin Witthaus, Witthaus, Robin
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #FOS: Mathematics #Number Theory (math.NT) #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.2208.12479

openalex publication_date 2022/08/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We extend Colmez's functor defined for GL₂(Q_p) to the category of finitely generated smooth admissible mod-p representations of the two-fold metaplectic cover of GL₂(Q_p). We compute the images of the absolutely irreducible genuine objects and obtain a bijection between the genuine supersingular representations and four-dimensional irreducible Galois representations invariant under twist by all characters of order two. Restricted to genuine objects, the extended functor naturally takes values in the category of what we call metaplectic Galois representations -- Galois representations with a certain extra structure encoding the aforementioned twist-invariance.

Related

• The mod-p representation theory of the metaplectic cover of GL₂(Q_p)
• Finiteness properties of generalized Montréal functors with applications to mod p representations of GL_n(ℚ_p)
• Irreducible admissible mod-p representations of metaplectic groups
• The characterization of theta-distinguished representations of GL_n
• A classification of the irreducible admissible genuine mod p representations of the metaplectic cover of p-adic SL(2)