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The Quarterly Journal of Mathematics Advance Access published online on June 4, 2009
The Quarterly Journal of Mathematics, doi:10.1093/qmath/hap020
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© 2009. Published by Oxford University Press. All rights reserved. For permissions, please email: journals.permissions@oxfordjournals.org

ANNIHILATORS OF PERMUTATION MODULES

S. Doty{dagger}

Mathematics and Statistics, Loyola University Chicago, Chicago, IL 60626, USA

K. Nyman {ddagger}

Mathematics Department, Willamette University, 900 State Street, Salem, OR 97301, USA

{dagger} Corresponding author. E-mail: doty{at}math.luc.edu; sdoty{at}luc.edu

Received 6 January 2009; revised 30 April 2009
  Abstract

Permutation modules are fundamental in the representation theory of symmetric groups Sn and their corresponding Iwahori–Hecke algebras H = H(Sn). We find an explicit combinatorial basis for the annihilator of a permutation module in the ‘integral’ case—showing that it is a cell ideal in Murphy's cell structure of H. The same result holds whenever H is semisimple, but may fail in the non-semisimple case.

{ddagger} E-mail: knyman{at}willamette.edu


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