Homomorphisms between Weyl modules for 𝑆𝐿₃(𝑘)

Cox, Anton; Parker, Alison

doi:10.1090/S0002-9947-06-03861-X

Homomorphisms between Weyl modules for $\operatorname {SL}_3(k)$
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by Anton Cox and Alison Parker PDF

Trans. Amer. Math. Soc. 358 (2006), 4159-4207 Request permission

Abstract:

We classify all homomorphisms between Weyl modules for $\operatorname {SL}_3(k)$ when $k$ is an algebraically closed field of characteristic at least three, and show that the $\operatorname {Hom}$-spaces are all at most one dimensional. As a corollary we obtain all homomorphisms between Specht modules for the symmetric group when the labelling partitions have at most three parts and the prime is at least three. We conclude by showing how a result of Fayers and Lyle on Hom-spaces for Specht modules is related to earlier work of Donkin for algebraic groups.

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