On intertwining operators for \(GL_ N(F)\), F a nonarchimedean local field
type: Item
instance of: scholarly article
title: On intertwining operators for \(GL_ N(F)\), F a nonarchimedean local field
zbMATH Open document ID: 0665.22006
DOI: 10.1215/S0012-7094-88-05712-2
author: David Manderscheid
author: Philip C. Kutzko
published in: Duke Mathematical Journal
publication date: 1988-01-01T00:00:00Z
review text: Let F be a nonarchimedean local field of residual characteristic p. As a first step toward a construction of the set of irreducible supercuspidal representations of \(GL_ N(F)\) when \(p| N\), the authors generalize a theorem of Howe to the wildly ramified case. More precisely let E be a finite-dimensional extension of F, let V be a finite-dimensional vector space over E and let \(\alpha\) be a primitive element of E/F with ``good arithmetic properties''. The main result asserts, roughly speaking, that the g in \(GL_ F(V)\) such that \(g\alpha g^{-1}=\alpha\) up to ``small terms'' lie in \(GL_ E(V)\) up to equally small terms. The paper is rather difficult to read because of its technical nature and of its numerous notations.
Mathematics Subject Classification ID: 22E50
Mathematics Subject Classification ID: 11S15
zbMATH DE Number: 4087937
zbMATH Keywords: nonarchimedean local field
zbMATH Keywords: irreducible supercuspidal representations
zbMATH Keywords: wildly ramified
reviewed by: Gilles Christol
MaRDI profile type: Publication
cites work: Hereditary orders, Gauss sums and supercuspidal representations of GLN.
cites work: Non-Abelian Congruence Gauss Sums and p -Adic Simple Algebras
cites work: Représentations cuspidales du groupe linéaire
cites work: Tamely ramified supercuspidal representations of \(Gl_n\)
cites work: Q3722752
cites work: Q5772619
cites work: Q5596900
cites work: Q3829748
cites work: Towards a Classification of the Supercuspidal Representations of Gl N
cites work: Local Constants and the Tame Langlands Correspondence
cites work: Q3856855
cites work: Algèbres de Hecke et induites de représentations cuspidales, pour GL (N).
full work available at URL: s0012-7094-88-05712-2
OpenAlex ID: W1974925575
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description: scientific article; zbMATH DE number 4087937