{"product_id":"admissible-dual-of-gln-via-compact-open-subgroups","title":"Admissible Dual of GL(N) via Compact Open Subgroups","description":"This work gives a full description of a method for analyzing the admissible complex representations of the general linear group G = Gl(N,F) 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.","brand":"Princeton University Press","offers":[{"title":"Default Title","offer_id":54222035091800,"sku":"9780691021140","price":107.99,"currency_code":"EUR","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0278\/1295\/4195\/files\/9780691021140_1b212231-f940-4c62-b5e3-4c7f0210413c.jpg?v=1776936642","url":"https:\/\/agendabookshop.com\/products\/admissible-dual-of-gln-via-compact-open-subgroups","provider":"Agenda Bookshop","version":"1.0","type":"link"}