  This paper consists of two prongs. Firstly, we prove that any Specht module
labelled by a 2-separated partition is semisimple and we completely determine
its decomposition as a direct sum of graded simple modules. Secondly, we apply
these results and other modular representation theoretic techniques on the
study of Kronecker coefficients and hence verify Saxl's conjecture for a large
new class of partitions.
