arXiv:0904.0787 [math.RT]AbstractReferencesReviewsResources
Weyl submodules in restrictions of simple modules
Published 2009-04-05Version 1
Let F be an algebraically closed field of characteristic p>0. Suppose that SL_{n-1}(F) is naturally embedded into SL_n(F) (either in the top left corner or in the bottom right corner). We prove that certain Weyl modules over SL_{n-1}(F) can be embedded into the restriction L(\omega)\downarrow_{SL_{n-1}(F)}, where L(\omega) is a simple SL_n(F)-module. This allows us to construct new primitive vectors in L(\omega)\downarrow_{\SL_{n-1}(F)} from any primitive vectors in the corresponding Weyl modules. Some examples are given to show that this result actually works.
Journal: Journal of Algebra 321 (2009), no. 5, 1453 -1462
Categories: math.RT
Subjects: 20G05
Keywords: simple modules, weyl submodules, restriction, primitive vectors, corresponding weyl modules
Tags: journal article
Related articles: Most relevant | Search more
Crystal bases and simple modules for Hecke algebras of type G(p,p,n)
The number of simple modules for the Hecke algebras of type G(r,p,n) (with an appendix by Xiaoyi Cui)
Stratifications of algebras with two simple modules