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The Complexity of the Lie Module

Published online by Cambridge University Press:  05 September 2013

Karin Erdmann ,
Kay Jin Lim  and
Kai Meng Tan
Karin Erdmann
Affiliation:
Mathematical Institute, University of Oxford, Oxford OX1 3LB, UK, (erdmann@maths.ox.ac.uk)
Kay Jin Lim
Affiliation:
Department of Mathematics, National University of Singapore, Block S17, 10 Lower Kent Ridge Road, Singapore 119076, Singapore, (limkj@ntu.edu.sg; tankm@nus.edu.sg)
Kai Meng Tan
Affiliation:
Department of Mathematics, National University of Singapore, Block S17, 10 Lower Kent Ridge Road, Singapore 119076, Singapore, (limkj@ntu.edu.sg; tankm@nus.edu.sg)
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Abstract

We show that the complexity of the Lie module Lie(n) in characteristic p is bounded above by m, where pm is the largest p-power dividing n, and, if n is not a p-power, is equal to the maximum of the complexities of Lie(pi) for 1≤i≤m.

Keywords

Lie modulep-modular representationsymmetric groupwreath productcomplexityPrimary 20C30
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 57 , Issue 2 , June 2014 , pp. 393 - 404
Copyright
Copyright © Edinburgh Mathematical Society 2014 

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