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Bernstein-Zelevinsky derivatives: a Hecke algebra approach
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.Comment: 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 update
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