相关论文: Exact Yangian Symmetry in the Classical Euler-Calo…

We discuss elliptic quantum Calogero-Moser-Sutherland models, including their relativistic generalizations due to Ruijsenaars and van Diejen, and the relations of these models to classes of special functions developed and explored in recent…

The classical $R$-matrix structure for the $n$-particle Calogero-Moser models with (type IV) elliptic potentials is investigated. We show there is no momentum independent $R$-matrix (without spectral parameter) when $n\ge4$. The assumption…

We introduce an odd supersymmetric version of the Kronecker elliptic function. It satisfies the genus one Fay identity and supersymmetric version of the heat equation. As an application we construct an odd supersymmetric extensions of the…

We investigate Yangian symmetry for the equations of motion and the action of the classical bi-scalar and supersymmetric fishnet models in four spacetime dimensions, and we subsequently discuss its applicability to planar correlation…

Studying the mirror symmetry of a Calabi-Yau threefold $X$ of the Reye congruence in $\mP^4$, we conjecture that $X$ has a non-trivial Fourier-Mukai partner $Y$. We construct $Y$ as the double cover of a determinantal quintic in $\mP^4$…

We demonstrate that in a certain gauge the elliptic Ruijsenaars--Schneider models admit Lax representation governed by the same dynamical $r$--matrix as their non--relativistic counterparts (Calogero--Moser models). This phenomenon was…

This paper is devoted to algebro-geometric study of infinite dimensional Lie bialgebras, which arise from solutions of the classical Yang-Baxter equation. We regard trigonometric solutions of this equation as twists of the standard Lie…

A computer algebra algoritm for solving the quantum Yang-Baxter equation is presented. It is based on the Taylor expansion of R-matrix which is developed up to the order \lambda^6. As an example the classification of 4x4 R-matrices is…

We present a method to construct "X" form unitary Yang-Baxter $\breve{R}$ matrices, which act on the tensor product space $V_{i}^{j_{1}}\otimes V_{i+1}^{j_{2}}$. We can obtain a set of entangled states for $(2j_{1}+1)\times…

The complete solutions of the spin generalization of the elliptic Calogero Moser systems are constructed. They are expressed in terms of Riemann theta-functions. The analoguous constructions for the trigonometric and rational cases are also…

We use the definition of the Calogero-Moser models as Hamiltonian reductions of geodesic motions on a group manifold to construct their $R$-matrices. In the Toda case, the analogous construction yields constant $R$-matrices. By contrast,…

A perfect Euler cuboid is a rectangular parallelepiped with integer edges and integer face diagonals whose space diagonal is also integer. The problem of finding such parallelepipeds or proving their non-existence is an old unsolved…

A method to construct the universal twist element using the constant quasiclassical unitary matrix solution of the Yang - Baxter equation is proposed. The method is applied to few known $R$ -matrices, corresponding to Lie (super) algebras…

A perfect Euler cuboid is a rectangular parallelepiped with integer edges, with integer face diagonals, and with integer space diagonal as well. Finding such parallelepipeds or proving their non-existence is an old unsolved mathematical…

Orthogonal or symplectic Yangians are defined by the Yang-Baxter $RLL$ relation involving the fundamental $R$ matrix with $so(n)$ or $sp(2m)$ symmetry. Simple $L$ operators with linear or quadratic dependence on the spectral parameter exist…

We review recent progress in the understanding of symmetries for scattering amplitudes in N=4 superconformal Yang-Mills theory. It is summarized how the superficial breaking of superconformal symmetry by collinear anomalies and the…

We construct a wide class of finite W-algebras as truncations of Yangians. These truncations correspond to algebra homomorphisms and allow to construct the W-algebras as exchange algebras, the R-matrix being the Yangian's one. As an…

We present a generalization of the master solution to the quantum Yang-Baxter equation (obtained recently in arXiv:1006.0651) to the case of multi-component continuous spin variables taking values on a circle. The Boltzmann weights are…

We study integrable dynamical systems described by a Lax pair involving a spectral parameter. By solving the classical Yang-Baxter equation when the R-matrix has two poles we show that they can be interpreted as natural motions on a twisted…

We derive several explicit formulae for finding infinitely many solutions of the equation $AXA=XAX$, when $A$ is singular. We start by splitting the equation into a couple of linear matrix equations and then show how the projectors…