LAUSR

For n ≥ a ≥ b , the tensor product V = ∧ a ( ℂ n ) ⊗ ∧ b ( ℂ n ) $V=\bigwedge ^{a}(\mathbb {C}^{n})\otimes \bigwedge ^{b}(\mathbb {C}^{n})$ has a natural filtration 0 = V m + 1 ⊆ V m ⊆⋯ ⊆ V 2 ⊆ V 1 ⊆ V 0 = V of Gl n submodules where m = min( n − a , b ) and V / V 1 is the Cartan product. For each 1 ≤ u ≤ m , we construct a basis for V u and a basis for the quotient V / V u . The elements in the basis for V u can be regarded as a generalization of the quadratic relations, and the elements in the basis for V / V u are parametrized by a set of skew tableaux satisfying a condition that cleanly extends the well known semistandardness condition defining a basis for V / V 1 .