Reductive pairs arising from representations
Group Theory
2014-12-31 v1
Abstract
Let G be a reductive algebraic group and V a G-module. We consider the question of when (GL(V), rho(G)) is a reductive pair of algebraic groups, where rho is the representation afforded by V. We first make some observations about general G and V, then specialise to the group SL2(K) with K algebraically closed of positive characteristic p. For this group we provide complete answers for the classes of simple and Weyl modules, the behaviour being determined by the base p expansion of the highest weight of the module. We conclude by illustrating some of the results from the first section with examples for the group SL3(K).
Cite
@article{arxiv.1412.8603,
title = {Reductive pairs arising from representations},
author = {Oliver Goodbourn},
journal= {arXiv preprint arXiv:1412.8603},
year = {2014}
}
Comments
Twelve pages, no figures. More detail is available in the author's PhD thesis