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.References
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Additional Information
- Anton Cox
- Affiliation: Centre for Mathematical Science, City University, Northampton Square, London, EC1V 0H, England
- Email: A.G.Cox@city.ac.uk
- Alison Parker
- Affiliation: School of Mathematics and Statistics F07, University of Sydney, NSW 2006, Australia
- Address at time of publication: Department of Mathematics, University of Leicester, Leicester, LE1 7RH, England
- Email: alisonp@maths.usyd.edu.au, aep24@mcs.le.ac.uk
- Received by editor(s): January 27, 2004
- Received by editor(s) in revised form: September 20, 2004
- Published electronically: April 11, 2006
- Additional Notes: The first author was partially supported by Nuffield grant scheme NUF-NAL 02
- © Copyright 2006 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 358 (2006), 4159-4207
- MSC (2000): Primary 20G05; Secondary 20C30
- DOI: https://doi.org/10.1090/S0002-9947-06-03861-X
- MathSciNet review: 2219015