A new presentation for Specht modules with distinct parts

Abstract

We obtain a new presentation for Specht modules whose conjugate shapes have strictly decreasing parts by introducing a linear operator on the space generated by column tabloids. The generators of the presentation are column tabloids and the relations form a proper subset of the Garnir relations of Fulton. The results in this paper extend earlier results of the authors and Stanley on Specht modules of staircase shape.

12 pages. This article generalizes Theorem 2.4 of arXiv:1710.00376. V2:small changes and corrections. V3: correction of an error in the proof of Theorem 2.5 without changing the structure of the proof