The construction of a class of presentations for Specht modules

Abstract

We build on the methods introduced by Friedmann, Hanlon, Stanley, and Wachs, and further developed by Brauner and Friedmann, to construct additional classes of presentations of Specht modules. We obtain these presentations by defining a linear operator which is a symmetrized sum of dual Garnir relations on the space of column tabloids. Our presentations apply to the vast majority of shapes of Specht modules.

arXiv comment24 pages; this article generalizes Theorem 2.4 or arXiv:1710.00376, Theorem 1.1 of arXiv:2303.00587, and Theorem 3.5 of arXiv:1803.10918; v2: minor revisions, version to appear in The Electronic Journal of Combinatorics