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In 1981, G. D. James proved two theorems about the decomposition matrices of Schur algebras involving the removal of the first row or column from a Young diagram. He established corresponding results for the symmetric group using the Schur functor. We apply James' techniques to prove that row removal induces an injection on the corresponding Ext 1 between simple modules for the Schur algebra. We then give a new proof of James' symmetric group result for partitions with the first part less than p. This proof lets us demonstrate that first-row removal induces an injection on Ext 1 spaces between these simple modules for the symmetric group. We conjecture that our theorem holds for arbitrary partitions. This conjecture implies the Kleshchev-Martin conjecture that Ext1 Σr (D λ , D λ ) = 0 for any simple module D λ in characteristic p ¬= 2. The proof makes use of an interesting fixed-point functor from Σ r -modules to Σ r-m -modules about which little seems to be known.

A row removal theorem for the Ext¹ quiver of symmetric groups and Schur algebras