Tunisian Journal of Mathematics

Tame multiplicity and conductor for local Galois representations

Colin J. Bushnell and Guy Henniart

Full-text: Access denied (no subscription detected)

However, an active subscription may be available with MSP at msp.org/tunis.

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text


Let F be a non-Archimedean locally compact field of residual characteristic p. Let σ be an irreducible smooth representation of the absolute Weil group WF of F and sw(σ) the Swan exponent of σ. Assume sw(σ)1. Let F be the inertia subgroup of WF and PF the wild inertia subgroup. There is an essentially unique, finite, cyclic group Σ, of order prime to p, such that σ(F)=Σσ(PF). In response to a query of Mark Reeder, we show that the multiplicity in σ of any character of Σ is bounded by sw(σ).

Article information

Tunisian J. Math., Volume 2, Number 2 (2020), 337-357.

Received: 16 September 2018
Revised: 8 May 2019
Accepted: 27 May 2019
First available in Project Euclid: 13 August 2019

Permanent link to this document

Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 11S15: Ramification and extension theory 11S37: Langlands-Weil conjectures, nonabelian class field theory [See also 11Fxx, 22E50] 22E50: Representations of Lie and linear algebraic groups over local fields [See also 20G05]

Local field tame multiplicity conductor bound primitive representation


Bushnell, Colin J.; Henniart, Guy. Tame multiplicity and conductor for local Galois representations. Tunisian J. Math. 2 (2020), no. 2, 337--357. doi:10.2140/tunis.2020.2.337. https://projecteuclid.org/euclid.tunis/1565661719

Export citation


  • C. J. Bushnell and A. Fröhlich, Gauss sums and $p$-adic division algebras, Lecture Notes in Mathematics 987, Springer, 1983.
  • C. J. Bushnell and G. Henniart, “Langlands parameters for epipelagic representations of $\mathrm{GL}_n$”, Math. Ann. 358:1–2 (2014), 433–463.
  • C. J. Bushnell and G. Henniart, “Higher ramification and the local Langlands correspondence”, Ann. of Math. $(2)$ 185:3 (2017), 919–955.
  • C. J. Bushnell and G. Henniart, “Local Langlands correspondence and ramification for Carayol representations”, preprint, 2019. To appear in Compositio Math.
  • G. Glauberman, “Correspondences of characters for relatively prime operator groups”, Canadian J. Math. 20 (1968), 1465–1488.
  • D. Gorenstein, Finite groups, 2nd ed., Amer. Math. Soc., Providence, RI, 2012.
  • G. Henniart, “Représentations du groupe de Weil d'un corps local”, Enseign. Math. $(2)$ 26:1-2 (1980), 155–172.
  • I. M. Isaacs, Character theory of finite groups, Amer. Math. Soc., Providence, RI, 2006. Corrected reprint of the 1976 original.
  • H. Koch, “Classification of the primitive representations of the Galois group of local fields”, Invent. Math. 40:2 (1977), 195–216.
  • M. Reeder, “Adjoint Swan conductors, I: The essentially tame case”, Int. Math. Res. Not. 2018:9 (2018), 2661–2692.
  • J. F. Rigby, “Primitive linear groups containing a normal nilpotent subgroup larger than the centre of the group”, J. London Math. Soc. 35 (1960), 389–400.
  • J.-P. Serre, Corps locaux, 2nd ed., Hermann, Paris, 1968.