Smooth Representations of GLm(D) VI: Semisimple Types

Autor:	Vincent Sécherre, Shaun Stevens
Rok vydání:	2011
Předmět:	Pure mathematics Hecke algebra Conjugacy class Multiplicative group Mathematics::Number Theory General Mathematics Affine transformation Locally compact space Type (model theory) Mathematics::Representation Theory Central simple algebra Spectrum (topology) Mathematics
Zdroj:	International Mathematics Research Notices. 2012:2994-3039
ISSN:	1687-0247 1073-7928
DOI:	10.1093/imrn/rnr122
Popis:	We give a complete description of the category of smooth complex representations of the multiplicative group of a central simple algebra over a locally compact nonarchimedean local field. More precisely, for each inertial class in the Bernstein spectrum, we construct a type and compute its Hecke algebra. The Hecke algebras that arise are all naturally isomorphic to products of affine Hecke algebras of type A. We also prove that, for cuspidal classes, the simple type is unique up to conjugacy.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::3dc967d6bbe186e234358f1803d74cab https://doi.org/10.1093/imrn/rnr122 Zobrazit plný text záznamu