In this paper, we describe a study into the explicit construction of irreducible representations of the Hecke algebra Hn(q) of type An−1 in the non-generic case where q is a root of unity. The approach is via the Specht modules of Hn(q) which are irreducible in the generic case, and possess a natural basis indexed by Young tableaux. The general framework in which the irreducible non-generic Hn(...

We generalise the lattice word condition from Young tableaux to all Kronecker and hence calculate a large new family of stable coefficients.

There are several results concerning double cosets of Young subgroups of symmetric groups which are often proved as corollaries of more general results about Coxeter groups. In this note we give a selection of these results and give them short combinatorial proofs. The replacement for the machinery of Coxeter groups consists of some simple combinatorial arguments involving tableaux. Inevitably ...

Let the sign of a skew standard Young tableau be the sign of the permutation you get by reading it row by row from left to right, like a book. We examine how the sign property is transferred by the skew Robinson-Schensted correspondence invented by Sagan and Stanley. The result is a remarkably simple generalization of the ordinary non-skew formula. The sum of the signs of all standard tableaux ...

We present some partial results surrounding two conjectures of Schützenberger on evacuations of Young tableaux.

There are several results concerning double cosets of Young subgroups of symmetric groups which are often proved as corollaries of more general results about Coxeter groups. In this note we give a selection of these results and give them the short combinatorial proofs they deserve. Our replacement for the machinery of Coxeter groups consists of some simple combinatorial arguments involving tabl...