Weight function for the quantum affine algebra Uq(A2(2))U_q(A_2^{(2)})

In this article, we give an explicit formula for the universal weight function of the quantum twisted affine algebra $U_q(A_2^{(2)})$. The calculations use the technique of projecting products of Drinfeld currents onto the intersection of Borel subalgebras of different types.Comment: 25 page

Gauss decomposition of trigonometric R-matrices

The general formula for the universal R-matrix for quantized nontwisted affine algebras by Khoroshkin and Tolstoy is applied for zero central charge highest weight modules of the quantized affine algebras. It is shown how the universal R-matrix produces the Gauss decomposition of trigonomitric R-matrix in tensor product of these modules. Explicit calculations for the simplest case of $A_1^{(1)}$ are presented. As a consequence new formulas for the trigonometric R-matrix with a parameter in tensor product of $U_q(sl_2)$-Verma modules are obtained.Comment: 14 page

Q-power function over Q-commuting variables and deformed XXX, XXZ chains

We find certain functional identities for the Gauss q-power function of a sum of q-commuting variables. Then we use these identities to obtain two-parameter twists of the quantum affine algebra U_q (\hat{sl}_2) and of the Yangian Y(sl_2). We determine the corresponding deformed trigonometric and rational quantum R-matrices, which then are used in the computation of deformed XXX and XXZ Hamiltonians.Comment: LaTeX, 12 page

Factorization of the Universal R-matrix for Uq(sl^2)U_q(\hat{sl}_2)

The factorization of the universal R-matrix corresponding to so called Drinfeld Hopf structure is described on the example of quantum affine algebra $U_q(\hat{sl}_2)$. As a result of factorization procedure we deduce certain differential equations on the factors of the universal ${\cal R}$-matrix, which allow to construct uniquely these factors in the integral form.Comment: 28 pages, LaTeX 2.09 using amssym.def and amssym.te

Three realizations of quantum affine algebra Uq(A2(2))U_q(A_2^{(2)})

In this article we establish explicit isomorphisms between three realizations of quantum twisted affine algebra $U_q(A_2^{(2)})$: the Drinfeld ("current") realization, the Chevalley realization and the so-called $RLL$ realization, investigated by Faddeev, Reshetikhin and Takhtajan.Comment: 15 page

Super-Yangian Y(gl(1|1)) and Its Oscillator Realization

On the basis of graded RTT formalism,the defining relation of the super-Yangian Y(gl(1|1)) is derived and its oscillator realization is constructed.Comment: 7 pages, latex, no figures, to appaer in the International Workshop on Frontiers in Quantum Field Theory,Urumqi,11-18,Augast,199