Bernstein-Zelevinsky derivatives: a Hecke algebra approach

2017/02/04 by Chan, Kei Yuen, Savin, Gordan · 1 citation
#11F70 #20C08 #22E50 #FOS: Mathematics #Number Theory (math.NT) #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.1702.01259

Abstract

Let G be a general linear group over a p-adic field. It is well known that Bernstein components of the category of smooth representations of G are described by Hecke algebras arising from Bushnell-Kutzko types. We describe the Bernstein components of the Gelfand-Graev representation of G by explicit Hecke algebra modules. This result is used to translate the theory of Bernstein-Zelevinsky derivatives in the language of representations of Hecke algebras, where we develop a comprehensive theory.

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