For a nilpotent linear transformation  of Jordan type l, let  be the subvariety of a Grassmannian whose generic point is the subspace spanned by the generic vectors for all cells of a skew tableau Tin l. A relation on the set of such tableaux of the same size is defined by the inclusions of these subvarieties in the Grassmannian; if We prove two theorems about this relation, and give a simple algorithm to construct the Littlewood-Richardson (LR) tableau dual to an LR-tableau.

Jordan types, Grassmannian, Littlewood-Richardson tableaux.