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A REMARK ON THE PERMUTATION REPRESENTATIONS AFFORDED BY THE EMBEDDINGS OF ${ \text{O} }_{2m}^{\pm } ({2}^{f} )$ IN ${\text{Sp} }_{2m} ({2}^{f} )$
Published online by Cambridge University Press: 19 September 2013
Abstract
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 ${ \mathrm{O} }_{2m}^{- } ({2}^{f} )$.
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- Research Article
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- Copyright ©2013 Australian Mathematical Publishing Association Inc.
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