title: Capelli bitableaux and Z-forms of general linear Lie superalgebras.
abstract: The combinatorics of the enveloping algebra UQ(pl(L)) of the general linear Lie superalgebra of a finite dimensional Z2-graded Q-vector space is studied. Three non-equivalent Z-forms of UQ(pl(L)) are introduced: one of these Z-forms is a version of the Kostant Z-form and the others are Lie algebra analogs of Rota and Stein's straightening formulae for the supersymmetric algebra Super[L P] and for its dual Super[L* P*]. The method is based on an extension of Capelli's technique of variabili ausiliarie to algebras containing positively and negatively signed elements.
authors.affiliation: Dipartimento di Matematica, Università di Bari, Bari, Italy.
authors.forename: A
authors.initials: A
authors.lastname: Brini
authors.forename: A G
authors.initials: AG
authors.lastname: Teolis