Some q-analogues of the Carter-Payne theorem
Abstract We prove a q-analogue of the Carter-Payne theorem for the two special cases corresponding to moving an arbitrary number of nodes between adjacent rows, or moving one node between an arbitrary number of rows. As a consequence, we show that these homomorphism spaces are one dimensional when q ≠ −1. We apply these results to complete the classification of the reducible Specht modules for the Hecke algebras of the symmetric groups when q ≠ −1. Our methods can also be used to determine certain other pairs of Specht modules between which there is a homomorphism. In particular, we describe the homomorphism space for an arbitrary partition μ.