相关论文: Yangians and transvector algebras
We consider the quiver Yangians associated to general affine Dynkin diagrams. Although the quivers are generically not toric, the algebras have some similar structures. The odd reflections of the affine Dynkin diagrams should correspond to…
In the previous paper, we constructed a homomorphism from the affine Yangian associated with $\widehat{\mathfrak{sl}}(n)$ to the standard degreewise completion of the affine Yangian associated with $\widehat{\mathfrak{sl}}(n+1)$. In this…
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…
We give a new proof of the fact that the super Yangian of general linear Lie superalgebra is isomorphic to the finite W-superalgebra of the general linear Lie superalgebra associated to a rectangular nilpotent element.
In this paper we study Yangians of sl(n|m) superalgebras. We derive the universal R-matrix and evaluate it on the fundamental representation obtaining the standard Yang R-matrix with unitary dressing factors. For m=0, we directly recover up…
We consider the (finite) $W$-algebra $W_{m|n}$ attached to the principal nilpotent orbit in the general linear Lie superalgebra $\mathfrak{gl}_{m|n}(\mathbb C)$. Our main result gives an explicit description of $W_{m|n}$ as a certain…
We focus on quiver Yangians for most generalized conifolds. We construct a coproduct of the quiver Yangian following the similar approach by Guay-Nakajima-Wendlandt. We also prove that the quiver Yangians related by Seiberg duality are…
We show an algebra morphism between Yangians and some finite W-algebras. This correspondence is nicely illustrated in the framework of the Non Linear Schrodinger hierarchy. For such a purpose, we give an explicit realization of the Yangian…
A famous result of Kostant states that the universal enveloping algebra of a semisimple complex Lie algebra is a free module over its center. We prove an analogue of this result for a class of filtered algebras and apply it to show 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 construct a non-trivial homomorphism from the Guay's affine Yangian to the universal enveloping algebra of non-rectangular $W$-algebras of type $A$. In order to construct the homomorphism, we extend the Guay's affine Yangian and its…
We derive some new presentations for the Yangian associated to the Lie algebra gl_n(C) that are adapted to parabolic subalgebras. At one extreme, the presentation is just the usual RTT presentation, whilst at the other extreme it is a…
We describe a Gauss decomposition for the Yangian Y(gl_{m|n}) of the general linear Lie superalgebra. This gives a connection between this Yangian and the Yangian of the classical Lie superalgebra Y(A(m-1,n-1)) (with m and n not equal)…
We construct a homomorphism from the affine Yangian $Y_{\hbar,\varepsilon+\hbar}(\widehat{\mathfrak{sl}}(n))$ to the affine Yangian $Y_{\hbar,\varepsilon}(\widehat{\mathfrak{sl}}(n+1))$ which is different from the one in arXiv:2312.09933.…
We classify the finite-dimensional irreducible representations of the super Yangian associated with the orthosymplectic Lie superalgebra ${\frak osp}_{2|2n}$. The classification is given in terms of the highest weights and Drinfeld…
The Lie superalgebra $\mathfrak{psl}(2|2)$ is recognized as a pretty special one in both mathematics and theoretical physics. In this paper, we present the Drinfeld realization of the Yangian algebra associated with the centrally extended…
The connections between Euler's equations on central extensions of Lie algebras and Euler's equations on the original, extended algebras are described. A special infinite sequence of central extensions of nilpotent Lie algebras constructed…
We show that some finite W-superalgebras based on gl(M|N) are truncation of the super-Yangian Y(gl(M|N)). In the same way, we prove that finite W-superalgebras based on osp(M|2n) are truncation of the twisted super-Yangians Y(gl(M|2n))^{+}.…
We construct generators of the center of the universal enveloping algebra of the complex orthogonal Lie algebra realized as the alternative matrices of size $n$. These elements are constructed in accordance with the Iwasawa decomposition of…
We prove several basic properties of the Yangian of the general linear Lie superalgebra.