Homomorphisms between Specht modules

In positive characteristic, the Specht modules S corresponding to partitions are not necessarily irreducible, and understanding their structure is vital to understanding the representation theory of the symmetric group. In this paper, we address the related problem of finding the spaces of homomorphisms between Specht modules. Indeed in 2], Carter and Payne showed that the space of homomorphisms from S to S is non-zero for certain pairs of partitions and where the Young diagram for is obtained from that for by moving several nodes from one row to another. We also consider partitions of this type, and, by explicitly examining certain combinations of semi-standard homomorphisms, we are able to give a constructive proof of the Carter–Payne theorem and to generalise it.Mathematics Subject Classification (2000): 20C30