On homomorphisms indexed by semistandard tableaux

Details On homomorphisms indexed by semistandard tableaux On homomorphisms indexed by semistandard tableaux

2011-01-17

arxiv.org/abs/1101.3192v3

Mathematics

Representation Theory

32 pages. This third version of the paper contains some comments on homomorphisms between the Specht modules defined by Dipper

Scientific paper

We study the homomorphism spaces between Specht modules for the Hecke algebras $\h$ of type $A$. We prove a cellular analogue of the kernel intersection theorem and a $q$-analogue of a theorem of Fayers and Martin and apply these results to give an algorithm which computes the homomorphism spaces $\Hom_{\h}(S^\mu,S^\lambda)$ for certain pairs of partitions $\lambda$ and $\mu$. We give an explicit description of the homomorphism spaces $\Hom_\h(S^\mu,S^\lambda)$ where $\h$ is an algebra over the complex numbers, $\lambda=(\lambda_1,\lambda_2)$ and $\mu$ is an arbitrary partition with $\mu_1 \geq \lambda_2$.

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