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arXiv · 0711.3219

Annihilators of permutation modules

Stephen Doty·Kathryn Nyman
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Abstract

Permutation modules are fundamental in the representation theory of symmetric groups $\Sym_n$ and their corresponding Iwahori--Hecke algebras $\He = \He(\Sym_n)$. 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 G.E. Murphy's cell structure of $\He$. The same result holds whenever $\He$ is semisimple, but may fail in the non-semisimple case.

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Stephen Doty, Kathryn Nyman. 2009-06-30. Annihilators of permutation modules. https://arxiv.org/abs/0711.3219

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