A simplified presentation of Specht modules.

We simplify a dual straightening algorithm which gives a presentation of Specht modules as a quotient of the space of column tabloids by dual Garnir relations. We show that this presentation can be generated by a single relation for each pair of columns of a tableau with ordered columns, thereby significantly reducing the number of generators given in the original construction. Our presentation applies to all Specht modules, and is of a similar nature to a recent result by Friedmann-Hanlon-Stanley-Wachs that applies to staircase partitions. We then discuss applications of our simplified presentation to a generalization of the multilinear component of the free Lie algebra studied by Friedmann, Hanlon, Stanley and Wachs.