Abstract
This paper describes parabolic induction, for smooth representations of finite length of the general linear group GL(N, F) of a non-archimedean local field F, in terms of a functor between categories of modules over certain affine Hecke algebras, using the categorical equivalences developed in the Bushnell-Kutzko classification of the admissible dual of GL(N, F). This result is used to prove that the Zelevinsky automorphism, which is an involutive automorphism on the representation ring of the category of smooth representations of finite length of GL(N, F), preserves the irreducible representations. The result also implies a simplification of the study of multiplicities of composition factors of induced representations. 1991 Mathematics Subject Classification: 11S37, 22E50.
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