A new presentation for Specht modules with distinct parts
Combinatorics
2025-02-10 v3
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.
Cite
@article{arxiv.2307.00587,
title = {A new presentation for Specht modules with distinct parts},
author = {Tamar Friedmann and Phil Hanlon and Michelle L. Wachs},
journal= {arXiv preprint arXiv:2307.00587},
year = {2025}
}
Comments
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