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Le Groupe GLn Tordu, Sur un Corps Fini

Published online by Cambridge University Press:  11 January 2016

J.-L. Waldspurger
J.-L. Waldspurger*
Affiliation:
CNRS-Institut de Mathématiques de Jussieu, 175, rue du Chevaleret 75013 Paris, France
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Abstract

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Let q be a finite field, G = GLn(q), θ be the outer automorphism of G, suitably normalized. Consider the non-connected group G ⋊ {1, θ} and its connected component = Gθ. We know two ways to produce functions on , with complex values and invariant by conjugation by G: on one hand, let π be an irreducible representation of G we can and do extend to a representation π+ of G ⋊ {1, θ}, then the restriction trace to of the character of π+ is such a function; on the other hand, Lusztig define character-sheaves a, whose characteristic functions ϕ(a) are such functions too. We consider only “quadratic-unipotent” representations. For all such representation π, we define a suitable extension π+, a character-sheave f(π) and we prove an identity trace = γ(π)ϕ(f(π)) with an explicit complex number γ(π).

Keywords

20C3320G40
Type
Research Article
Information
Nagoya Mathematical Journal , Volume 182: Special Issue Celebrating the 60th Birthday of George Lusztig , June 2006 , pp. 313 - 379
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 2006

References

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