The Admissible Dual of GL(N) via Compact Open SubgroupsColin J. Bushnell Philip C. KutzkoLabel: Princeton University PressDescription: This work gives a full description of a method for analyzing the admissible complex representations of the general linear group G = Gl(NF) of a non-Archimedean local field F in terms of the structure of these representations when they are restricted to certain compact open subgroups of G. The authors define a family of representations of these compact open subgroups which they call simple types. The first example of a simple type the trivial type is the trivial character of an Iwahori subgroup of G. The irreducible representations of G containing the trivial simple type are classified by the simple modules over a classical affine Hecke algebra. Via an isomorphism of Hecke algebras this classification is transferred to the irreducible representations of G containing a given simple type. This leads to a complete classification of the irreduc-ible smooth representations of G including an explicit description of the supercuspidal representations as induced representations. A special feature of this work is its virtually complete reliance on algebraic methods of a ring-theoretic kind. A full and accessible account of these methods is given here.
