Specht module cohomology and integral designs

Abstract

We aim to construct an element satisfying Hemmer's combinatorial criterion for $H^1({\mathfrak{S}}_n,S^{\lambda })$ to be non-vanishing. In the process, we discover an unexpected and surprising link between the combinatorial theory of integral designs and the representation theory of the symmetric groups.

16 pages, based on results of my PhD thesis prepared at the University of Cambridge

Cited by in corpus (1)

• A combinatorial approach to first degree cohomology of Specht modules