CLASSICAL AND QUANTUM SL(1-VERTICAL-BAR-2) SUPERALGEBRAS, CASIMIR-OPERATORS AND QUANTUM CHAIN HAMILTONIANS

We examine in this paper the two parameter deformed superalgebra U-qs( sl(1\2)) and use the results in the construction of quantum chain Hami ltonians. This study is done both in the framework of the Serre presen tation and in the R-matrix scheme of Faddeev, Reshetikhin, and Takhtaj an (FRT). We show that there exists an infinite number of Casimir oper ators, indexed by integers p greater than or equal to 2 in the undefor med case and by p is an element of Z in the deformed case, which obey quadratic relations. The construction of the dual superalgebra of func tions of SL(qs) (1\2) is also given and higher tenser product represen tations are discussed. Finally, we construct quantum chain Hamiltonian s based on the Casimir operators. In the deformed case we find two Ham iltonians which describe deformed t-J models. (C) 1995 American Instit ute of Physics.