Related papers: Rational K-matrices and representations of twisted…
This is the first in a series of papers investigating the relationship between the twisted equivariant K-theory of a compact Lie group G and the "Verlinde ring" of its loop group. In this paper we set up the foundations of twisted…
We extend our study of the field-theoretic description of matrix-vector models and the associated many-body problems of one dimensional particles with spin. We construct their Yangian-su(R) invariant Hamiltonian. It describes an interacting…
We discuss some aspects of the deformed W-algebras W_{q,t}[g]. In particular, we derive an explicit formula for the Kac determinant, and discuss the center when t^2 is a primitive k-th root of unity. The relation of the structure of…
We develop the representation theory of shifted quantum affine algebras $\mathcal{U}_q^\mu(\hat{\mathfrak{g}})$ and of their truncations which appeared in the study of quantized K-theoretic Coulomb branches of 3d $N = 4$ SUSY quiver gauge…
We show an algebra morphism between Yangians and some finite W-algebras. This correspondence is nicely illustrated in the framework of the Non Linear Schrodinger hierarchy. For such a purpose, we give an explicit realization of the Yangian…
We determine the intertwiners of a family of Onsager coideal subalgebras of the quantum affine algebra $U_p(A^{(1)}_{n-1})$ in the fundamental representations and $U_p(B^{(1)}_{n}), U_p(D^{(1)}_{n}), U_p(D^{(2)}_{n+1})$ in the spin…
We derive and classify all solutions of the boundary Yang-Baxter equation (or the reflection equation) for the 19-vertex model associated with $U_q(\widehat{sl_2})$. Integrable $XXZ$ spin-1 chain hamiltonian with general boundary…
We associate to every matroid M a polynomial with integer coefficients, which we call the Kazhdan-Lusztig polynomial of M, in analogy with Kazhdan-Lusztig polynomials in representation theory. We conjecture that the coefficients are always…
We study the quantum vertex algebraic framework for the Yangians of RTT-type and the braided Yangians associated with Hecke symmetries, introduced by Gurevich and Saponov. First, we construct several families of modules for the…
We discuss the integrability structure of deformed, four-dimensional N=4 super Yang-Mills theories using Yangians. We employ a recent procedure by Beisert and Roiban that generalizes the beta deformation of Lunin and Maldacena to produce…
The construction elements of the factorised form of the Yang-Baxter R operator acting on generic representations of q-deformed sl(n+1) are studied. We rely on the iterative construction of such representations by the restricted class of…
It is pointed out that the apparent presence of the fusing rule for purely elastic scattering theories in theories with dynamical Yangian invariance implies beautiful and hitherto unseen structure in the finite-dimensional representation…
Based on the RTT relation for a given rational $R$-matrix the {\em Yangian} and truncated {\em Yangian} are discussed. The former can be used to generate the long-range interaction models, whereas the latter can be related to the…
We present the classification of the most general regular solutions to the boundary Yang-Baxter equations for vertex models associated with non-exceptional affine Lie algebras. Reduced solutions found by applying a limit procedure to the…
We define quantum determinants in Quantum Matrix Algebras, related to couples of compatible braidings following the scheme from [G]. We establish relations between these determinants and the so-called column-(row-)determinants, often used…
Yang-Baxterising a braid group representation associated with multideformed version of $GL_{q}(N)$ quantum group and taking the corresponding $q\rightarrow 1$ limit, we obtain a rational $R$-matrix which depends on $\left ( 1+ {N(N-1) \over…
Integrable boundary states can be built up from pair annihilation amplitudes called $K$-matrices. These amplitudes are related to mirror reflections and they both satisfy Yang Baxter equations, which can be twisted or untwisted. We relate…
We introduce a representation theory of q-Lie algebras defined earlier in \cite{DG1}, \cite{DG2}, formulated in terms of braided modules. We also discuss other ways to define Lie algebra-like objects related to quantum groups, in…
In this paper we work out the RTT-realization for the Yangian algebra of the Hubbard model and AdS/CFT correspondence. We find that this Yangian algebra is of a non-standard type in which the levels of the Yangian mix. The crucial feature…
The odd reflections are an effective tool in the Lie superalgebra representation theory, as they relate non-conjugate Borel subalgebras. We introduce analogues of the odd reflections for the Yangian ${\rm Y}({\frak gl}_{m|n})$ and use them…