On the algebra A_{\hbar,\eta}(osp(2|2)^{(2)}) and free boson representations

A two-parameter quantum deformation of the affine Lie super algebra $osp(2|2)^{(2)}$ is introduced and studied in some detail. This algebra is the first example associated with nonsimply-laced and twisted root systems of a quantum current algebra with the structure of a so-called infinite Hopf family of (super)algebras. A representation of this algebra at $c=1$ is realized in the product Fock space of two commuting sets of Heisenberg algebras.Comment: 14 pages, LaTe

q-deformed Supersymmetric t-J Model with a Boundary

The q-deformed supersymmetric t-J model on a semi-infinite lattice is diagonalized by using the level-one vertex operators of the quantum affine superalgebra $U_q[\hat{sl(2|1)}]$. We give the bosonization of the boundary states. We give an integral expression of the correlation functions of the boundary model, and derive the difference equations which they satisfy.Comment: LaTex file 18 page

Eigenvalues of Ruijsenaars-Schneider models associated with An−1A_{n-1} root system in Bethe ansatz formalism

Ruijsenaars-Schneider models associated with $A_{n-1}$ root system with a discrete coupling constant are studied. The eigenvalues of the Hamiltonian are givein in terms of the Bethe ansatz formulas. Taking the "non-relativistic" limit, we obtain the spectrum of the corresponding Calogero-Moser systems in the third formulas of Felder et al [20].Comment: Latex file, 25 page

Infinite Hopf family of elliptic algebras and bosonization

Elliptic current algebras E_{q,p}(\hat{g}) for arbitrary simply laced finite dimensional Lie algebra g are defined and their co-algebraic structures are studied. It is shown that under the Drinfeld like comultiplications, the algebra E_{q,p}(\hat{g}) is not co-closed for any g. However putting the algebras E_{q,p}(\hat{g}) with different deformation parameters together, we can establish a structure of infinite Hopf family of algebras. The level 1 bosonic realization for the algebra E_{q,p}(\hat{g}) is also established.Comment: LaTeX, 11 pages. This is the new and final versio

Entanglement detection beyond the CCNR criterion for infinite-dimensions

In this paper, in terms of the relation between the state and the reduced states of it, we obtain two inequalities which are valid for all separable states in infinite-dimensional bipartite quantum systems. One of them provides an entanglement criterion which is strictly stronger than the computable cross-norm or realignment (CCNR) criterion.Comment: 11 page