An upper bound on conductors for pairs
type: Item
instance of: scholarly article
title: An upper bound on conductors for pairs
zbMATH Open document ID: 0884.11049
author: Colin J. Bushnell
author: Guy Henniart
published in: Journal of Number Theory
publication date: 1997-08-17T00:00:00Z
review text: Let \(a\), \(b\), \(c\) be the exponents (defined by means of the \(\varepsilon\) factors) of the irreducible admissible representations \(\pi\), \(\rho\), \(\pi\times\rho\) of \(GL(m,F)\), \(GL(n,F)\), \(GL(m,F)\times GL(n,F)\). Here \(F\) is a \(p\)-adic field. It is shown that \(c\leq na+mb-\min(a,b)\) using the essential vector in the Whittaker model in the generic case.
Mathematics Subject Classification ID: 11S37
Mathematics Subject Classification ID: 20G25
zbMATH DE Number: 1048747
zbMATH Keywords: conductors of representations of \(GL(n)\) over a \(p\)-adic field
reviewed by: Yuval Z. Flicker
MaRDI profile type: Publication
full work available at URL: jnth.1997.2142
OpenAlex ID: W2093995672
cites work: Induced representations of reductive ${\germ p}$-adic groups. I
cites work: Zeta functions of simple algebras
cites work: Q4853473
cites work: Rankin-Selberg Convolutions
cites work: Conducteur des représentations du groupe linéaire
cites work: \({\mathcal D}\)-elliptic sheaves and the Langlands correspondence
cites work: On an explicit formula for class-$1$ “Whittaker functions” on $GL_n $ over $\beta $-adic fields
cites work: Induced representations of reductive ${\germ p}$-adic groups. II. On irreducible representations of ${\rm GL}(n)$
DOI: 10.1006/JNTH.1997.2142
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description: scientific article; zbMATH DE number 1048747