Related papers: Yangian, Truncated Yangian and Quantum Integrable …
We introduce parabolic presentations of twisted Yangians of types AI and AII, interpolating between the R-matrix presentation and the Drinfeld presentation. Then we formulate and provide parabolic presentations for the shifted twisted…
We construct a series of rational representations of Y(gl_n) and intertwining operators between them. We find explicit expressions for the images of highest-weight vectors under the intertwining operators. Finally, we state a conjecture…
Three introductory lectures: on Yangians and their representations; on Yangian symmetry in 1+1D integrable (bulk) field theory; and on the effect of a boundary upon this symmetry.
We establish a parabolic presentation of the extended Yangian $\X(\mathfrak{g}_{N})$ associated with the Lie algebras $\mathfrak{g}_{N}$ of type $B$ and $C$, parameterized by a symmetric composition $\nu$ of $N$. By formulating a block…
We describe several methods of constructing R-matrices that are dependent upon many parameters, for example unitary R-matrices and R-matrices whose entries are functions. As an application, we construct examples of R-matrices with…
In the first part, we introduce the notion of fractional statistics in the sense of Haldane. We illustrate it on simple models related to anyon physics and to integrable models solvable by the Bethe ansatz. In the second part, we describe…
We present a connection between W-algebras and Yangians, in the case of gl(N) algebras, as well as for twisted Yangians and/or super-Yangians. This connection allows to construct an R-matrix for the W-algebras, and to classify their…
We introduce a $N_c\times N_c$ matrix model with $\mathcal{N}=2$ supersymmetries and show its relation to the topological rigid string and the topological YM$_2$. This allows to connect the latter two theories directly. Moreover the…
In this paper we discuss a constructive approach to check whether a constant Hamiltonian is Yang-Baxter integrable. We then apply our method to long-range interactions and find the Lax operator and $R$-matrix of the two-loop SU(2) sector in…
Yang-Baxter relations symmetric with respect to the ortho-symplectic superalgebras are studied. We start from the formulation of graded algebras and the linear superspace carrying the vector (fundamental) representation of the…
Various aspects of the theory of quantum integrable systems are reviewed. Basic ideas behind the construction of integrable ultralocal and nonultralocal quantum models are explored by exploiting the underlying algebraic structures related…
Novel constructions of empirical controllability and observability gramians for nonlinear systems for subsequent use in a balanced truncation style of model reduction are proposed. The new gramians are based on a generalisation of the…
The aim of this review is to present the list of by now a significant collection of quantum integrable models, ultralocal as well as nonultralocal, in a systematic way stressing on their underlying unifying algebraic structures. We restrict…
q-bosonic realization of the underlying Yang-Baxter algebra is identified for a series of quantum integrable systems, including some new models like two-mode q-bosonic model leading to a coupled two-component derivative NLS model, wide…
It is known that noncommutative Yang-Mills is equivalent to IIB matrix model with a noncommutative background, which is interpreted as a twisted reduced model. In noncommutative Yang-Mills, long range interactions can be seen in nonplanar…
The quantum Yang-Baxter equation admits generalisations to systems of Yang-Baxter type equations called Yang-Baxter systems. Starting from algebra structures, we propose new constructions of some constant as well as the spectral-parameter…
R-matrix is explicitly constructed for simplest representations of the Ding-Iohara-Miki algebra. The calculation is straightforward and significantly simpler than the one through the universal R-matrix used for a similar calculation in the…
We describe the construction of trigonometric R-matrices corresponding to the (multiplicity-free) tensor product of any two irreducible representations of a quantum algebra $U_q(\G)$. Our method is a generalization of the tensor product…
Condensed ionic systems are described in the framework of a combined approach that takes into account both long-range and short-range interactions. Short-range interaction is expressed in terms of mean potentials and long-range interaction…
Using the representation theory of Yangians we construct the rational R-matrix which takes values in the adjoint representation of SU(n). From this we derive an integrable SU(n) spin chain with lattice spins transforming under the adjoint…