  A graded poset structure is defined for the sets of Littlewood-Richardson
(LR) tableaux that count the multiplicity of an irreducible GL(n)-module in the
tensor product of irreducibles indexed by a sequence of rectangular partitions.
This poset generalizes the cyclage poset on column-strict tableaux defined by
Lascoux and Schutzenberger, and its grading function generalizes the charge
statistic. It is shown that the polynomials obtained by enumerating LR tableaux
by shape and the generalized charge, are the Poincare polynomials of isotypic
components of the certain modules supported in the closure of a nilpotent
conjugacy class.
