Iterating lowering operators

For an algebraically closed base field of characteristic p>0, a new algorithm to construct some non-zero GL(n-1)-high weight vectors of irreducible rational GL(n)-modules is suggested. It is based on successively applying Kleshchev's lowering operators to GL(n-1)-high weight vectors already obtained.Comment: This is the extended version of my paper in JPA

On extensions and branching rules for modules close to completely splittable

New exact modular branching rules are obtained for modules over the symmetric groups that are close to completely splittable modules. These results are based on some upper bounds for the Ext^1-spaces between simple modules