Homomorphisms between Weyl modules for SL₃(k)

2005/08/26 by Anton Cox, Cox, Anton, Alison Parker +1
Mathematics · #20C30 #20G05 #FOS: Mathematics #Representation Theory (math.RT) #math.RT #msc:20C30 #msc:20G05

paper · pdf · doi:10.48550/arxiv.math/0508520

41 pages, 2 colour figures, 25 black and white figures

arxiv created 2005/08/26 · arxiv updated 2009/12/01

Abstract

We classify all homomorphisms between Weyl modules for SL₃(k) when k is an algebraically closed field of characteristic at least three, and show that the 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.

Related

• Large Dimension Homomorphism Spaces Between Specht Modules for Symmetric Groups
• Relating homomorphism spaces between Specht modules of different degrees
• On homomorphisms between Weyl modules: The case of a column transposition
• Large dimensional homomorphism spaces between Weyl modules and Specht modules
• Specht Modules for Weyl Groups