Unicity of types and local Jacquet--Langlands correspondence

2022/05/11 by Yamamoto, Yuki
#22E50 #FOS: Mathematics #Number Theory (math.NT) #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.2205.05252

Abstract

Let F be a non-archimedean local field. For any irreducible representation π of an inner form G'=GL_m(D) of G=GL_N(F), there exists an irredubile representation of a maximal compact open subgroup in G' which is also a type for π. Then we can consider the problem whether these types are unique or not in some sense. If such types for π are unique, we say π has the strong unicity property of types. On the other hand, there exists a correspondence connecting irreducible representations of G' and G, called the Jacquet--Langland correspondence. In this paper, we study the ralation between the strong unicity of types and the Jacquet--Langlands correspondence.

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