Weyl submodules in restrictions of simple modules
Representation Theory
2009-04-07 v1
Abstract
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.
Cite
@article{arxiv.0904.0787,
title = {Weyl submodules in restrictions of simple modules},
author = {Vladimir Shchigolev},
journal= {arXiv preprint arXiv:0904.0787},
year = {2009}
}