Related papers: Super Yangians in characteristic $2$
We discovered new hidden symmetry of the one-dimensional Hubbard model. We showthat the one-dimensional Hubbard model on the infinite chain has the infinite-dimensional algebra of symmetries. This algebra is a direct sum of two $ sl(2)…
The centrally extended su(2|2) superalgebra is an asymptotic symmetry of the light-cone string sigma model on AdS5 x S5. We consider an evaluation representation of the conventional Yangian built over a particular 16-dimensional long…
In this paper we review recent results on symmetries in N=4 super Yang-Mills theory. Symmetries are of invaluable help in studying and constraining the scattering amplitudes, and there has been a lot of progress in recent years concerning…
We are concerned with finite-dimensional irreducible representations of the Yangians associated with the orthosymplectic Lie superalgebras ${\frak osp}_{2n+1|2m}$. Every such representation is highest weight and we use embedding theorems…
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 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…
Let $\mathfrak{g}$ be a complex semisimple Lie algebra with associated Yangian $Y_\hbar\mathfrak{g}$. In the mid-1990s, Khoroshkin and Tolstoy formulated a conjecture which asserts that the algebra $\mathrm{D}Y_\hbar\mathfrak{g}$ obtained…
Analogs of the classical Sylvester theorem have been known for matrices with entries in noncommutative algebras including the quantized algebra of functions on GL(N) and the Yangian for gl(N). We prove a version of this theorem for the…
Drinfeld Yangian of a queer Lie superalgebra is defined as the quantization of a Lie bisuperelgebra of twisted polynomial currents. An analogue of the new system of generators of Drinfeld is being constructed. It is proved for the partial…
We define supersymmetric Yang-Mills theory on an arbitrary two-dimensional lattice (polygon decomposition) with preserving one supercharge. When a smooth Riemann surface $\Sigma_g$ with genus $g$ emerges as an appropriate continuum limit of…
Remarkable subalgebras of the Yangian for gl_n called the shifted Yangians were introduced in a recent work by Brundan and Kleshchev in relation to their study of finite W-algebras. In particular, in that work a classification of…
We give several formulas for the character of an arbitrary irreducible finite--dimensional representation for the Yangian of sl_2.
In this paper, we establish the first rigorous framework for the Drinfeld super Yangian associated with an exceptional Lie superalgebra, which lacks a classical Lie algebraic counterpart. Specifically, we systematically investigate the…
We classify irreducible representations of finite $W$-algebra of the queer Lie superalgebra $Q(n)$ associated with the principal nilpotent coadjoint orbits. We use this classification and our previous results to obtain a classification of…
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 define affine Super Yangian $Y_{\hbar}(\hat{sl}(m|n), \Pi) $ for affine special linear superalgebra $\hat{sl}(m|n)$ and arbitrary system of simple roots $\Pi$ in terms of minimalistic system of generators. We also consider Drinfeld…
Laumon moduli spaces are certain smooth closures of the moduli spaces of maps from the projective line to the flag variety of $GL_n$. We construct the action of the Yangian of $sl_n$ in the cohomology of Laumon spaces by certain natural…
Following V. Toledano-Laredo and S. Gautam approach we construct isomorphism between super $\hbar$-Yangian $Y_{\hbar}(A(m,n))$ of special linear superalgebra and quantum loop superalgebra $U_{\hbar}(LA(m,n))$.
We present the algebraic framework for the quantization of the classical bosonic charge algebra of maximally extended (N=16) supergravity in two dimensions, thereby taking the first steps towards an exact quantization of this model. At the…
In 2016, Etingof defined the notion of a Yangian in a symmetric tensor category and posed the problem to study them in the context of Deligne categories. This problem was studied by Kalinov in 2020 for the Yangian $Y(\mathfrak{gl}_t)$ of…