相关论文: Yangians, Integrable Quantum Systems and Dorey's r…

We show how equivariant volumes of tensor product quiver varieties of type A are given by matrix elements of vertex operators of centrally extended doubles of Yangians, and how they satisfy in some cases the rational, level 1, quantum…

We present a quantum version of the construction of the KZ system of equations as a flat connection on the spaces of coinvariants of representations of tensor products of Kac-Moody algebras. We consider here representations of a tensor…

In this paper a class of new quantum groups is presented: deformed Yangians. They arise from rational solutions of the classical Yang-Baxter equation of the form $c_2 /u + const$ . The universal quantum $R$-matrix for a deformed Yangian is…

Several years ago, it was proposed that the usual solutions of the Yang-Baxter equation associated to Lie groups can be deduced in a systematic way from four-dimensional gauge theory. In the present paper, we extend this picture, fill in…

Based on the (quantum) twisted Yangians, integrable systems with special boundary conditions, called soliton non-preserving (SNP), may be constructed. In the present article we focus on the study of subalgebras of the (quantum) twisted…

We study right exact tensor products on the category of finitely presented functors. As our main technical tool, we use a multilinear version of the universal property of so-called Freyd categories. Furthermore, we compare our constructions…

We establish several results concerning tensor products, q-characters, and the block decomposition of the category of finite-dimensional representations of quantum affine algebras in the root of unity setting. In the generic case, a Weyl…

It is argued that the partition of a quantum system into subsystems is dictated by the set of operationally accessible interactions and measurements. The emergence of a multi-partite tensor product structure of the state-space and the…

We present a conjecture on the irreducibility of the tensor products of fundamental representations of quantized affine algebras. This conjecture implies in particular that the irreducibility of the tensor products of fundamental…

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…

Similarity transformations and eigenvalue relations of monodromy operators composed of Jordan-Schwinger type L matrices are considered and used to define Yangian symmetric correlators of n-dimensional theories. Explicit expressions are…

Complicated mathematical equations involving products of tensors with permutation symmetries, frequently encountered in fields such as general relativity and quantum chemistry (e.g., equations in high-order coupled cluster theories),…

We study unital operator spaces endowed with a partially defined product. We give a matrix-norm characterization of such products that allows for a representation theorem where the partial product is realized as composition of operators on…

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,…

The twisted q-Yangians are coideal subalgebras of the quantum affine algebra associated with gl(N). We prove a classification theorem for finite-dimensional irreducible representations of the twisted q-Yangians associated with the…

The purpose of this paper is to present an interpretation for the decomposition of the tensor product of two or more irreducible representations of GL(N) in terms of a system of quantum particles. Our approach is based on a certain…

Let $\mathfrak{g}$ be a complex semisimple Lie algebra with associated Yangian $Y_\hbar\mathfrak{g}$. In the mid-1990s, Khoroshkin and Tolstoy formulated a conjecture which asserts that the algebra $\mathrm{D}Y_\hbar\mathfrak{g}$ obtained…

We consider typical finite dimensional complex irreducible representations of a basic classical simple Lie superalgebra, and give a sufficient condition on when unique factorization of finite tensor products of such representations hold. We…

We study the Yangian symmetry of the multicomponent Quantum Nonlinear Schrodinger hierarchy in the framework of the Quantum Inverse Scattering Method. We give an explicit realization of the Yangian generators in terms of the deformed…

In this paper, we first establish a connection between Yangians and the unique formal solution of the quantum hypergeometric differential equations at irregular singularities. We then realize the Stokes matrices of the hypergeometric…