Weyl submodules in restrictions of simple modules

Details Weyl submodules in restrictions of simple modules Weyl submodules in restrictions of simple modules

2009-04-05

arxiv.org/abs/0904.0787v1

Journal of Algebra 321 (2009), no. 5, 1453 -1462

Mathematics

Representation Theory

Scientific paper

10.1016/j.jalgebra.2008.11.034

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.

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