Related papers: Twisted Yangians and folded W-algebras
We construct a class of new Lie algebras by generalizing the one-variable Lie algebras generated by the quadratic conformal algebras (or corresponding Hamiltonian operators) associated to Poisson algebras and a quasi-derivation found by Xu.…
The minimal irreducible representations of $U_q[gl(m|n)]$, i.e. those irreducible representations that are also irreducible under $U_q[osp(m|n)]$ are investigated and shown to be affinizable to give irreducible representations of the…
We give several formulas for the character of an arbitrary irreducible finite--dimensional representation for the Yangian of sl_2.
We describe the structure of the algebraic group of automorphisms of all simple finite dimensional Lie superalgebras. Using this and \'etale cohomology considerations, we list all different isomorphism classes of the corresponding twisted…
We deal with the classification problem of finite-dimensional representations of so called Askey--Wilson algebra in the case when $q$ is not a root of unity. We classify all representations satisfying certain property, which ensures…
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 associate vertex operator algebras to $(p,q)$-webs of interfaces in the topologically twisted $\mathcal{N}=4$ super Yang-Mills theory. Y-algebras associated to trivalent junctions are identified with truncations of…
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…
We use the Gauss decomposition of the generator matrix in the $R$-matrix presentation of the Yangian for the orthosymplectic Lie superalgebra ${\frak osp}_{N|2m}$ to produce its Drinfeld-type presentation. The results rely on a…
We study the equivariant homology of the generalized Steinberg variety of type C and show that there exists a surjective algebra homomorphism from the twisted Yangian of type $\AIII_{2n}^{(\tau)}$ to it.
Take the matrix Lie superalgebra $gl_{N|N}$ with the standard generators $E_{ij}$ where $i,j=-N,...,-1,1,...,N$. Define an involutive automorphism of $gl_{N|N}$ by sending $E_{ij}$ to $E_{-i,-j}$. Then the corresponding twisted subalgebra…
This paper completes a series devoted to explicit constructions of finite-dimensional irreducible representations of the classical Lie algebras. Here the case of odd orthogonal Lie algebras (of type B) is considered (two previous papers…
We observe that over an algebraically closed field, any finite-dimensional algebra is the endomorphism algebra of an m-cluster-tilting object in a triangulated m-Calabi-Yau category, where m is any integer greater than 2.
It is well-known that the Gauss decomposition of the generator matrix in the $R$-matrix presentation of the Yangian in type $A$ yields generators of its Drinfeld presentation. Defining relations between these generators are known in an…
Let $\Lambda$ be a graded self-injective algebra. We describe its smash product $\Lambda# k\mathbb Z^*$ with the group $\mathbb Z$, its Beilinson algebra and their relationship. Starting with $\Lambda$, we construct algebras with finite…
We proceed to study infinite-dimensional symmetries in two-dimensional squashed Wess-Zumino-Novikov-Witten (WZNW) models at the classical level. The target space is given by squashed S^3 and the isometry is SU(2)_L x U(1)_R. It is known…
The symmetries of the twisted XXZ spin-chain (alias the twisted six-vertex model) at roots of unity are investigated. It is shown that when the twist parameter is chosen to depend on the total spin an infinite-dimensional non-abelian…
This paper introduces the notion of twisted toric manifolds which is a generalization of one of symplectic toric manifolds, and proves the weak Delzant type classification theorem for them. The computation methods for their fundamental…
We show that a wide class of $W$-(super)algebras, including $W_N^{(N-1)}$, $U(N)$-superconformal as well as $W_N$ nonlinear algebras, can be linearized by embedding them as subalgebras into some {\em linear} (super)conformal algebras with…
In these introductory lectures we discuss the topic of Yangian symmetry from various perspectives. Forming the classical counterpart of the Yangian and an extension of ordinary Noether symmetries, first the concept of nonlocal charges in…