[3:2]-pairs of symmetric group algebras and their intermediate defect 4 blocks

In this paper we study [3:2]-pairs of symmetric group algebras and their ‘intermediate’ block in detail. The aim is to understand how one block of a [3:2]-pair can inherit two properties—the Ext-quiver being bipartite and the principal indecomposable modules having a common Loewy length 7—from the other. We establish some sufficient conditions for this inheritance, and verify these conditions for some special blocks.