Some $q$-analogues of the Certer-Payne theorem

Details Some $q$-analogues of the Certer-Payne theorem Some $q$-analogues of the Certer-Payne theorem

2006-04-10

arxiv.org/abs/math/0604216v1

Mathematics

Representation Theory

23 pages

Scientific paper

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 $q \neq -1$. We apply these results to complete the classification of the reducible Specht modules for the Hecke algebras of the symmetric groups when $q \neq-1$. 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 from the trivial module to an arbitrary Specht module.

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