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Twisted Dickson–Mui invariants and the Steinberg module multiplicity

Published online by Cambridge University Press:  18 March 2011

JINKUI WAN  and
WEIQIANG WANG
JINKUI WAN
Affiliation:
Department of Mathematics, Beijing Institute of Technology, Beijing, 100081, P.R. China. e-mail: [email protected]
WEIQIANG WANG
Affiliation:
Department of Mathematics, University of Virginia, Charlottesville, VA 22904, U.S.A. e-mail: [email protected]
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Abstract

We determine the invariants, with arbitrary determinant twists, of the parabolic subgroups of the finite general linear group GLn(q) acting on the tensor product of the symmetric algebra S•(V) and the exterior algebra ∧•(V) of the natural GLn(q)-module V. In addition, we obtain the graded multiplicity of the Steinberg module of GLn(q) in S•(V) ⊗ ∧•(V), twisted by an arbitrary determinant power.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 151 , Issue 1 , July 2011 , pp. 43 - 57
Copyright
Copyright © Cambridge Philosophical Society 2011

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