@inbook{8cf22d775b6c4dd59d4c58fd69444231,

title = "Explicit local Jacquet-Langlands correspondence: The non-dyadic wild case",

abstract = "Let F be a non-Archimedean locally compact field of residual characteristic p with p ≠ 2. Let n be a power of p and let G be an inner form of the general linear group GLn (F ). We give a transparent parametrization of the irreducible, totally ramified, cuspidal representations of G of parametric degree n. We show that the parametrization is respected by the Jacquet-Langlands correspondence, relative to any other inner form. This expresses the Jacquet-Langlands correspondence for such representations within a single, compact formula.",

keywords = "And phrases. Local Jacquet-Langlands correspondence, Cuspidal representation, Endo-class, Simple character",

author = "Bushnell, {Colin J.} and Guy Henniart",

note = "Publisher Copyright: {\textcopyright} 2019 American Mathematical Society.; Conference on Representation Theory and Algebraic Geometry held in honor of Joseph Bernstein, 2017 ; Conference date: 11-06-2017 Through 16-06-2017",

year = "2019",

doi = "10.1090/pspum/101/01790",

language = "English",

isbn = "9781470442842",

series = "Proceedings of Symposia in Pure Mathematics",

publisher = "American Mathematical Society",

pages = "45--72",

editor = "Avraham Aizenbud and Dmitry Gourevitch and Lapid, {Erez M.} and David Kazhdan",

booktitle = "Representations of Reductive Groups - Conference in honor of Joseph Bernstein Representation Theory and Algebraic Geometry, 2017",

address = "United States",

}