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On decomposition numbers and Alvis–Curtis duality

Published online by Cambridge University Press:  01 November 2007

BERND ACKERMANN  and
SIBYLLE SCHROLL
BERND ACKERMANN
Affiliation:
Inst.f.Algebra u.Zahlentheorie, Universität Stuttgart, 70550 Stuttgart, Germany. email: ackermann@mathematik.uni-stuttgart.de
SIBYLLE SCHROLL*
Affiliation:
Mathematical Institute, 24-29 St Giles, Oxford OX1 3LB. email: schroll@maths.ox.ac.uk
*
†The second author acknowledges support through a Marie Curie Fellowship.
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Abstract

We show that for general linear groups GLn(q) as well as for q-Schur algebras the knowledge of the modular Alvis–Curtis duality over fields of characteristic ℓ, ℓ ∤ q, is equivalent to the knowledge of the decomposition numbers.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 143 , Issue 3 , November 2007 , pp. 509 - 520
Copyright
Copyright © Cambridge Philosophical Society 2007

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