Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4597400 | Journal of Pure and Applied Algebra | 2009 | 21 Pages |
Abstract
Let G be a universal Chevalley group over an algebraically closed field and Uâ be the subalgebra of Dist(G) generated by all divided powers Xα,m with α<0. We conjecture an algorithm to determine if FeÏ+â 0, where FâUâ, Ï is a dominant weight and eÏ+ is a highest weight vector of the Weyl module Î(Ï). This algorithm does not use bases of Î(Ï) 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.
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Vladimir Shchigolev,