Submodule structure of some Weyl modules and the cohomology for

Abstract

Abstract We describe the formal characters of some Weyl modules for simply connected and semisimple algebraic groups of type Dl over an algebraically closed field of characteristic where h is the Coxeter number, in the terms of the formal characters of simple modules. We also compute some extensions and cohomology of simple modules associated with these Weyl modules. To prove the main results we use Jantzen’s sum formula. In the singular case, we obtain several new examples of simple Weyl modules.