Specht Module

A Specht module is the symmetric-group module associated with a partition of , constructed inside the permutation module on row tabloids by taking the span of polytabloids. A row tabloid identifies tableaux differing only by permutations within rows. A polytabloid is the signed sum of its tabloid over permutations within columns. Over the complex numbers, the modules give all irreducible representations of . The partitions and give the trivial and sign representations, respectively. Tensor squares of these modules are central to the tensor square conjecture and Saxl conjecture.