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The spherical building and regular semisimple elements

Published online by Cambridge University Press:  17 April 2009

G.I. Lehrer
G.I. Lehrer
Affiliation:
Department of Pure Mathematics, University of Sydney, Sydney, New South Wales 2006, Australia.
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Abstract

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Let G be a connected reductive algebraic group defined over a finite field k. The finite group G(k) of k-rational points of G acts on the spherical building B(G), a polyhedron which is functorially associated with G. We identify the subspace of points of B(G) fixed by a regular semisimple element s of G(k) topologically as a subspace of a sphere (apartment) in B(G) which depends on an element of the Weyl group which is determined by s. Applications include the derivation of the values of certain characters of G(k) at s by means of Lefschetz theory. The characters considered arise from the action of G(k) on the cohomology of equivariant sheaves over B(G).

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 27 , Issue 3 , June 1983 , pp. 361 - 379
Copyright
Copyright © Australian Mathematical Society 1983

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