For any removable e-small straight shape moved to an earlier component with matching residues, there is a nonzero positive-degree homomorphism between the corresponding graded Specht modules that maps the generator to a single standard basis vector.
Dixon, Some results concerning Verma modules , Ph.D
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A generalization of Carter-Payne homomorphisms
For any removable e-small straight shape moved to an earlier component with matching residues, there is a nonzero positive-degree homomorphism between the corresponding graded Specht modules that maps the generator to a single standard basis vector.