Related papers: Drinfel'd Twists and Algebraic Bethe Ansatz
We construct sets of structure matrices for the semi-dynamical reflection algebra, solving the Yang-Baxter type consistency equations extended by the action of an automorphism of the auxiliary space. These solutions are parametrized by…
The Drinfled realization of quantum affine algebras has been tremendously useful since its discovery. Combining techniques of Beck and Nakajima with our previous approach, we give a complete and conceptual proof of the Drinfeld realization…
The affine quantum Schur algebra is a certain important infinite dimensional algebra whose representation theory is closely related to that of quantum affine $\frak{gl}_n$. Finite dimensional irreducible modules for the affine quantum Schur…
Integrable open quantum spin-chain transfer matrices constructed from trigonometric R-matrices associated to affine Lie algebras $\hat g$, and from certain K-matrices (reflection matrices) depending on a discrete parameter p, were recently…
We find all the diagonal $K$-matrices for the $R$-matrix associated with the minimal representation of the exceptional affine algebra $G^{(1)}_2$. The corresponding transfer matrices are diagonalized with a variation of the analytic Bethe…
A quantum integrable spin chain model associated with the $G_2$ exceptional Lie algebra is studied. By using the fusion technique, the closed recursive relations among the fused transfer matrices are obtained. These identities allow us to…
We present an "algebraic treatment" of the analytical Bethe Ansatz. For this purpose, we introduce abstract monodromy and transfer matrices which provide an algebraic framework for the analytical Bethe Ansatz. It allows us to deal with a…
We discuss applications of the $q$-characters to the computation of the $R$-matrices. In particular, we describe the $R$-matrix acting in the tensor square of the first fundamental representation of E$_8$ and in a number of other cases,…
We establish the $Q \widetilde{Q}$-systems for the twisted quantum affine algebras that were conjectured in arXiv:1606.05301. We develop the representation theory of Borel subalgebra of twisted quantum affine algebras and we construct their…
A class of $\mathfrak{o}_{2n+1}$-invariant quantum integrable models is investigated in the framework of algebraic Bethe ansatz method. A construction of the $\mathfrak{o}_{2n+1}$-invariant Bethe vector is proposed in terms of the Drinfeld…
We give a detailed description of the adjoint representation of Drinfeld's twist element, as well as of its coproduct, for $su_{q}(2)$. We also discuss, as applications, the computation of the universal R-matrix in this representation and…
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…
We study quantized enveloping algebras called twisted Yangians. They are analogues of the Yangian Y(gl(N)) for the classical Lie algebras of B, C, and D series. The twisted Yangians are subalgebras in Y(gl(N)) and coideals with respect to…
Quantum affine reflection algebras are coideal subalgebras of quantum affine algebras that lead to trigonometric reflection matrices (solutions of the boundary Yang-Baxter equation). In this paper we use the quantum affine reflection…
We study integrable models solvable by the nested algebraic Bethe ansatz and possessing GL(3)-invariant R-matrix. We obtain determinant representations for form factors of off-diagonal entries of the monodromy matrix. These representations…
We lift the lattice of translations in the extended affine Weyl group to a braid group action on the quantum affine algebra. This action fixes the Heisenberg subalgebra pointwise. Loop like generators are found for the algebra which satisfy…
The integrable XXZ alternating spin chain with generic non-diagonal boundary terms specified by the most general non-diagonal K-matrices is studied via the off-diagonal Bethe Ansatz method. Based on the intrinsic properties of the fused…
In this survey, we review some of the recent connections between the representation theory of (untwisted) quantum affine algebras and the representation theory of current algebras. We mainly focus on the finite-dimensional representations…
Let $U_q(\hat{\cal G})$ be a quantized affine Lie algebra. It is proven that the universal R-matrix $R$ of $U_q(\hat{\cal G})$ satisfies the celebrated conjugation relation $R^\dagger=TR$ with $T$ the usual twist map. As applications, braid…
We consider quantum spin chains arising from $N$-fold tensor products of the fundamental evaluation representations of $Y(sl_n)$ and $U_q(\hat{sl_n})$. Using the partial $F$-matrix formalism from the seminal work of Maillet and Sanchez de…