Bernstein-Zelevinsky derivatives: a Hecke algebra approach
Representation Theory
2017-05-23 v2 Number Theory
Abstract
Let be a general linear group over a -adic field. It is well known that Bernstein components of the category of smooth representations of are described by Hecke algebras arising from Bushnell-Kutzko types. We describe the Bernstein components of the Gelfand-Graev representation of 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.
Cite
@article{arxiv.1702.01259,
title = {Bernstein-Zelevinsky derivatives: a Hecke algebra approach},
author = {Kei Yuen Chan and Gordan Savin},
journal= {arXiv preprint arXiv:1702.01259},
year = {2017}
}
Comments
21 pages, extending part of arXiv:1605.05130. v2: a new appendix is added for the projectivity of the Gelfand-Graev representation, and references are updated