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Bulletin of the London Mathematical Society Advance Access originally published online on December 15, 2006
Bulletin of the London Mathematical Society 2007 39(1):133-137; doi:10.1112/blms/bdl024
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© 2006 London Mathematical Society

Counting the discrete series for GL(n)

Colin J. Bushnell

Department of Mathematics
King's College London
Strand
London WC2R 2LS
United Kingdom
colin.bushnell{at}kcl.ac.uk

Guy Henniart

Université de Paris-Sud
Laboratoire de Mathématiques d’Orsay
Orsay Cedex, F-91405
CNRS
Orsay Cedex, F-91405
France
Guy.Henniart{at}math.u-psud.fr

Received 19 April 2005. Revision received 13 December 2005.

Let F be a non-Archimedean local field. Let n ≥ 1, j ≥ 0 be integers. This paper gives an exact formula for the number of equivalence classes of irreducible smooth representations of GLn(F) which are square-integrable mod centre, satisfy a certain condition on the central character, and admit a fixed vector for the jth principal congruence subgroup of the maximal compact subgroup Formula .


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