The Admissible Dual of Gl(n) Via Compact Open Subgroups. (Am-129), Volume 129 - (Annals of Mathematics Studies) by C Bushnell & P C Kutzko
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<p/><br></br><p><b> Book Synopsis </b></p></br></br><p>This work gives a full description of a method for analyzing the admissible complex representations of the general linear group <i>G</i> = <i>Gl(N, F)</i> of a non-Archimedean local field <i>F</i> in terms of the structure of these representations when they are restricted to certain compact open subgroups of <i>G</i>. The authors define a family of representations of these compact open subgroups, which they call <i>simple types.</i> The first example of a simple type, the "trivial type," is the trivial character of an Iwahori subgroup of <i>G</i>. The irreducible representations of <i>G</i> 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 <i>G</i> containing a given simple type. This leads to a complete classification of the irreduc-ible smooth representations of <i>G</i>, 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.</p><p/><br></br><p><b> About the Author </b></p></br></br><b>Colin J. Bushnell</b> is Professor of Mathematics at King's College, London. <i>Philip C. Kutzko</i> is Professor of Mathematics at the University of Iowa.
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