Related papers: Orthosymplectic Yangians

We classify the "finite-dimensional" irreducible representations of the Yangians $Y(\mathfrak{gl}_t)$ and $Y(\mathfrak{sl}_t)$. These are associative ind-algebras in the Deligne category $\textbf{Rep}(GL_t)$, which generalize the regular…

In this paper we investigate trigonometric vertex models associated with solutions of the Yang-Baxter equation which are invariant relative to q-deformed superalgebras sl(r|2m)^(2), osp(r|2m)^(1) and osp(r=2n|2m)^(2). The associated…

Two type of superization of the Jordanian r-matrix for the Lie algebra sl(2) are considered. One type is associated with the Lie superalgebra sl(1|1) and another type is associated with the orthosymplectic Lie superalgebra osp(1|2).…

A new class of infinite dimensional representations of the Yangians $Y(\frak{g})$ and $Y(\frak{b})$ corresponding to a complex semisimple algebra $\frak{g}$ and its Borel subalgebra $\frak{b}\subset\frak{g}$ is constructed. It is based on…

Longitudinally polarized, unpolarized and forward-backward mass differential cross sections for Drell-Yan lepton-pair production by arbitrary vector bosons are calculated in next-to-leading order (NLO) QCD. Analytical results are presented…

The exotic quantum double and its universal R-matrix for quantum Yang-Baxter equation are constructed in terms of Drinfeld's quantum double theory.As a new quasi-triangular Hopf algebra, it is much different from those standard quantum…

We continue our investigation of the nonlinear SUSY for complex potentials started in the Part I (math-ph/0610024) and prove the theorems characterizing its structure in the case of non-diagonalizable Hamiltonians. This part provides the…

We use the Dunkl operator approach to construct one dimensional integrable models describing N particles with internal degrees of freedom. These models are described by a general Hamiltonian belonging to the center of the Yangian or the…

We introduce symplectic structures on "Lie pairs" of (real or complex) algebroids as studied by Chen, Stienon and the second author (From Atiyah classes to homotopy Leibniz algebras, arXiv:1204.1075), encompassing homogeneous symplectic…

We will discuss an integrable structure for weakly coupled superconformal Yang-Mills theories, describe certain equivalences for the Yangian algebra, and fill a technical gap in our previous study of this subject.

We formulate and establish a super duality which connects parabolic categories $O$ between the ortho-symplectic Lie superalgebras and classical Lie algebras of $BCD$ types. This provides a complete and conceptual solution of the irreducible…

We study certain linear and antilinear symmetry generators and involution operators associated with pseudo-Hermitian Hamiltonians and show that the theory of pseudo-Hermitian operators provides a simple explanation for the recent results of…

We study the relationship between cyclic homology of Jordan superalgebras and second cohomologies of their Tits-Kantor-Koecher Lie superalgebras. In particular, we focus on Jordan superalgebras that are Kantor doubles of bracket algebras.…

We study the convolution algebra $H^{G\times \CC^{*}}_{*}(Z)$ of $G$-equivariant homology group on the Steinberg variety of type B/C and define an algebra $\widetilde{Y}$ that maps to $H^{G\times \CC^{*}}_{*}(Z)$. The Drinfeld new…

This paper deals with symmetry phenomena for solutions of the Dirichlet problem involving semilinear PDEs on Riemannian domains. We shall present a rather general framework where the symmetry problem can be formulated and provide some…

The evaluation homomorphisms from the super Yangian $\Ymn$ to the universal enveloping algebra $\U(\gl_{m|n})$ allows one to regard the covariant tensor module of $\gl_{m|n}$ as $\Ymn$ modules. We study simple quotients of the submodules…

In this survey, we explore how superorthogonality amongst functions in a sequence $f_1,f_2,f_3,\ldots$ results in direct or converse inequalities for an associated square function. We distinguish between three main types of…

The cosmological compactification of D=10, N=1 supergravity-super-Yang-Mills theory obtained from superstring theory is studied. The constraint of unbroken N=1 supersymmetry is imposed. A duality transformation is performed on the resulting…

The classification of the octonionic realizations of the one-dimensional extended supersymmetries is here furnished. These are non-associative realizations which, albeit inequivalent, are put in correspondence with a subclass of the already…

Let $\mathfrak{g}$ be a finite-dimensional simple Lie algebra over $\mathbb{C}$, and let $Y_{\hbar}(\mathfrak{g})$ be the Yangian of $\mathfrak{g}$. In this paper, we study the sets of poles of the rational currents defining the action of…