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.
Annihilators of permutation modules
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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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Rook sums in the symmetric group algebra
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.