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We use the presentation of the Specht modules given by Kleshchev-Mathas-Ramto derive results about Specht modules. In particular, we determine allhomomorphisms from an arbitrary Specht module to a fixed Specht modulecorresponding to any hook partition. Along the way, we give a completedescription of the action of the standard KLR generators on the hook Spechtmodule. This work generalizes a result of James.

Homomorphisms from an arbitrary Specht module to one corresponding to a hook