A Decomposition of the Set of Subspaces Stable Under a Nilpotent Transformation.

For a nilpotent linear transformationf:V → Vof Jordan type λ, letS(T) be the set off-stable subspacesWofVassociated with an LR (Littlewood–Richardson) tableauT. We show that (i)S(T) is a disjoint union of locally closed sets parametrized by LR-fillings ofT, each of which is birationally isomorphic to an affine space, and that (ii) a~conjecture of Shimomura on semistandardd-tableaux in a rectangular diagram is true. [ABSTRACT FROM PUBLISHER]