Oscillator Realization of Higher-U(m,n)-Spin Algebras of W(infinity)-type and Quantized Simplectic Diffeomorphisms

This article is a further contribution to our research [M.Calixto J.Phys.A33(2000)L69] into a class of infinite-dimensional Lie algebras L_\infty(m,n)generalizing the standard W_\infty algebra, viewed as a tensor operator algebra of SU(1,1) in a group-theoretic framework. Here we interpret L_\infty(m,n)either as infinite continuations of pseudo-unitary symmetries or as "higher-U(m,n)-spin extensions" of the diffeomorphism algebra diff(m,n). We also provide a deeper mathematical interconnection between Poisson (and symplectic diffeomorphism) algebras of functions on coadjoint orbits of pseudo-unitary groups U(m,n) and the classical limit of the corresponding tensor operator (and group) algebras. As potential applications we comment on the formulation of integrable higher-dimensional dynamical (field) systems and gauge theories of higher-extended objects. Some remarks on non-commutative geometry are also made