Young-Capelli symmetrizers in superalgebras.
Let Super(n)[U [unk] V] be the nth homogeneous subspace of the supersymmetric algebra of U [unk] V, where U and V are Z(2)-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 End(K)(Super(n)[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.
Dipartimento di Matematica, Universita di Bari, 70125 Bari, Italy.
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