Deformed Jacobson Generators of the Algebra Uq[sl(n+1)] and Their Fock Representations

A description of the quantum algebra U_q[sl(n + 1)] via a new set of generators, called deformed Jacobson generators, is given. It provides an alternative to the canonical description of U_q[sl(n + 1)] in terms of Chevalley generators. The Jacobson generators satisfy trilinear commutation relations and define U_q[sl(n + 1)] as a deformed Lie triple system. Fock representations are constructed and the action of the Jacobson generators on the Fock basis is written down. Finally, Dyson and Holstein-Primakoff realizations are given.