Young—Capelli symmetrizers in superalgebras

Let Supern [U [unk]V ] be then th homogeneous subspace of the supersymmetric algebra ofU [unk]V , whereU andV are Z2 -graded vector spaces over a field K of characteristic zero. The actions of the general linear Lie superalgebras pl(U ) and pl(V ) span two finite-dimensional K-subalgebras B and [unk] of EndK (Supern [U [unk]V ]) that are the centralizers of each other. Young—Capelli symmetrizers and Young—Capelli *-symmetrizers give rise to K-linear bases of B and [unk] containing orthogonal systems of idempotents; thus they yield complete decompositions of B and [unk] into minimal left and right ideals, respectively.