A local criterion for Weyl modules for groups of type A |
| |
Authors: | Vladimir Shchigolev |
| |
Institution: | Department of Algebra, Faculty of Mathematics, Lomonosov Moscow State University, Leninskiye Gory, Moscow, 119899, Russia |
| |
Abstract: | Let G be a universal Chevalley group over an algebraically closed field and U− be the subalgebra of generated by all divided powers Xα,m with α<0. We conjecture an algorithm to determine if , where F∈U−, ω is a dominant weight and is a highest weight vector of the Weyl module Δ(ω). This algorithm does not use bases of Δ(ω) and is similar to the algorithm for irreducible modules that involves stepwise raising the vector under investigation. For an arbitrary G, this conjecture is proved in one direction and for G of type A in both. |
| |
Keywords: | 20G05 |
本文献已被 ScienceDirect 等数据库收录! |
|