Compressed Straight Tableaux and a Distributive Lattice of Representations

Abstract

dedicated to the memory of gian-carlo rota A new``compressed straight'' basis for the polynomial ring Z[t i, j ] is constructed. This basis is then employed to study the lattice of representations generated by the representations associated with row-convex shapes under the operations of intersection and linear span. Applications to ascertaining the Cohen Macaulay property for rings associated to elements of this lattice are also given. Academic Press