A simplified presentation of Specht modules

Abstract

Fulton and Kraskiewicz gave a presentation of Specht modules as a quotient of the space of column tabloids by dual Garnir relations. We simplify this presentation by showing that it 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 show that our presentation implies the Friedmann-Hanlon-Stanley-Wachs presentation.

Final version appearing in the Journal of Pure and Applied Algebra

References in corpus (5)

• Algebraic structures on parallel M2-branes
• Three-Algebras and N=6 Chern-Simons Gauge Theories
• n-ary algebras: a review with applications
• Orbifold Singularities, Lie Algebras of the Third Kind (LATKes), and Pure Yang-Mills with Matter
• On a generalization of Lie($k$): a CataLAnKe theorem