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A REMARK ON THE PERMUTATION REPRESENTATIONS AFFORDED BY THE EMBEDDINGS OF ${ \text{O} }_{2m}^{\pm } ({2}^{f} )$ IN ${\text{Sp} }_{2m} ({2}^{f} )$

Part of: Other groups of matrices Permutation groups

Published online by Cambridge University Press:  19 September 2013

SIMON GUEST ,
ANDREA PREVITALI  and
PABLO SPIGA
SIMON GUEST*
Affiliation:
Mathematics, University of Southampton, Highfield, Southampton SO17 1BJ, UK
ANDREA PREVITALI
Affiliation:
Dipartimento di Matematica e Applicazioni, University of Milano-Bicocca, Via Cozzi 53, 20125 Milano, Italy email andrea.previtali@unimib.it
PABLO SPIGA
Affiliation:
Dipartimento di Matematica e Applicazioni, University of Milano-Bicocca, Via Cozzi 53, 20125 Milano, Italy email pablo.spiga@unimib.it
*
✉s.d.guest@soton.ac.uk
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Abstract

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We show that the permutation module over $ \mathbb{C} $ afforded by the action of ${\mathrm{Sp} }_{2m} ({2}^{f} )$ on its natural module is isomorphic to the permutation module over $ \mathbb{C} $ afforded by the action of ${\mathrm{Sp} }_{2m} ({2}^{f} )$ on the union of the right cosets of ${ \mathrm{O} }_{2m}^{+ } ({2}^{f} )$ and ${ \mathrm{O} }_{2m}^{- } ({2}^{f} )$.

Keywords

permutation groupspermutation character

MSC classification

Secondary: 20B05: General theory for finite groups 20H30: Other matrix groups over finite fields
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 89 , Issue 2 , April 2014 , pp. 331 - 336
Copyright
Copyright ©2013 Australian Mathematical Publishing Association Inc. 

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