Young--Capelli Symmetrizers in Superalgebras

Let Supern[U ⊗ V] be the nth homogeneous subspace of the supersymmetric algebra of U ⊗ V, where U and V are [Note: See the image of page 775 for this formatted text] Z2-graded vector spaces over a field [Note: See the image of page 775 for this formatted text] K of characteristic zero. The actions of the general linear Lie superalgebras pl(U) and pl(V) span two finite-dimensional [Note: Equation omitted. See the image of page 775 for this equation.] that are the centralizers of each other. Young--Capelli symmetrizers and Young--Capelli *-symmetrizers give rise to [Note: See the image of page 775 for this formatted text] K-linear bases of [Note: Equation omitted. See the image of page 775 for this equation.] containing orthogonal systems of idempotents; thus they yield complete decompositions of [Note: Equation omitted. See the image of page 775 for this equation.] into minimal left and right ideals, respectively.