Related papers: Modular orthogonal Yangians
We introduce super Yangian double $DY_\hbar[gl(m|n)]$ and its central extension $\widehat{DY_\hbar[gl(m|n)]}$. We give their defining relations in terms of current generators and obtain Drinfeld comultiplication.
Yangian-like algebras, associated with current R-matrices, different from the Yang ones, are introduced. These algebras are of two types. The so-called braided Yangians are close to the Reflection Equation algebras, arising from involutive…
In this note, we consider the twisted Yangians $\text{Y}(\mathfrak{g}_N)$ associated with the orthogonal and symplectic Lie algebras $\mathfrak{g}_N=\mathfrak{o}_N,\mathfrak{sp}_N$. First, we introduce a certain subalgebra…
The Yangian double $\text{DY}_{\hbar}(\mathfrak{g}_N)$ is introduced for the classical types of $\mathfrak{g}_N=\mathfrak{o}_{2n+1}$, $\mathfrak{sp}_{2n}$, $\mathfrak{o}_{2n}$. Via the Gauss decomposition of the generator matrix, the…
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…
The Yangian of the strange Lie superalgebras in Drinfel'd realization is defined. The current system generators and defining relations are described.
Central extension $\DYg$ of the Double of the Yangian is defined for a simple Lie algebra ${\bf g}$ with complete proof for ${\bf g} =sl_2$. Basic representations and intertwining operators are constructed for $\DY2$.
We study the double Yangian associated with the Lie superalgebra $\mathfrak{gl}_{m|n}$. Our main focus is on establishing the Poincar\'{e}-Birkhoff-Witt Theorem for the double Yangian and constructing its central elements in the form of…
We introduce the $h$-adic quantum vertex algebras associated with the rational $R$-matrix in types $B$, $C$ and $D$, thus generalizing the Etingof--Kazhdan's construction in type $A$. Next, we construct the algebraically independent…
We introduce a Drinfeld presentation for the super-Yangian $\mathrm{Y}(\mathfrak{q}_n)$ associated with the queer Lie superalgebra $\mathfrak{q}_n$. The Drinfeld generators of $\mathrm{Y}(\mathfrak{q}_n)$ are obtained through a block Gauss…
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 an analogue of the composition of the Cherednik and Drinfeld functor for twisted Yangians. Our definition is based on the Howe duality, and originates from the centralizer construction of twisted Yangians due to Olshanski.…
We give the principal realization of the twisted Yangians of orthogonal and symplectic types. The new bases are interpreted in terms of discrete Fourier transform over the cyclic group Z_N.
We study the truncated shifted Yangian $Y_{n,l}(\sigma)$ over an algebraically closed field $\mathbb{k}$ of characteristic $p > 0$, which is known to be isomorphic to the finite $W$-algebra $U(\mathfrak{g}, e)$ associated to a corresponding…
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…
Let \Y be a derived algebraic stack satisfying some mild conditions. The purpose of this paper is three-fold. First, we introduce and study H(\Y), a monoidal DG category that might be regarded as a categorification of the ring of…
We construct a new presentation of the twisted Yangian of type $D$ with a finite number of generators. By using this presentation, we propose a new definition of the twisted affine Yangian of type $D$.
This is a review paper on the algebraic structure and representations of the A type Yangian and the B, C, D types twisted Yangians. Some applications to constructions of Casimir elements and characteristic identities for the corresponding…
We construct a Hopf superalgebra structure for a Drinfeld super Yangian of Lie superalgebra $B(m,n)$ relative to all possible choices of Borel subalgebras. In order to do this we introduce a simplified definition of Drinfeld super Yangians.
We formulate a family of algebras, twisted Yangians (of simply-laced quasi-split type) in Drinfeld type current generators and defining relations. These new algebras admit PBW type bases and are shown to be a deformation of twisted current…