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Annihilators of permutation modules

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arxiv 0711.3219 v5 pith:FIYSO7X6 submitted 2007-11-20 math.RT math.GR

Stephen Doty , Kathryn Nyman This is my paper · ORCID
classification math.RTmath.GR
keywords permutationcasecellmodulesalgebrasannihilatorannihilatorsbasis
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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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  1. Rook sums in the symmetric group algebra

    math.CO 2025-07 conditional novelty 6.0 of 10

    Rook sums in the symmetric group algebra satisfy an explicit product rule, have linearly factorable minimal polynomials, and generate ideals whose sizes count pattern-avoiding permutations.

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