相关论文: Super-Schur Polynomials for Affine Super Yangian $…

We suggest an ansatz for representation of affine Yangian $Y(\hat{ \mathfrak{gl}}_1)$ by differential operators in the triangular set of time-variables ${\bf P}_{a,i}$ with $1\leqslant i\leqslant a$, which saturates the MacMahon formula for…

We define a class of $Y(sl_{(m|n)})$ Yangian invariant Haldane-Shastry (HS) like spin chains, by assuming that their partition functions can be written in a particular form in terms of the super Schur polynomials. Using some properties of…

We consider algebras acting on Schur and Q-Schur polynomials, corresponding to Kadomtsev-Petviashvili (KP) and BKP hierarchies. We present them in the spirit of affine Yangians, paying special attention to commutative subalgebras, box…

In this paper, we define the affine super Yangian $Y_{\varepsilon_1,\varepsilon_2}(\widehat{\mathfrak{sl}}(m|n))$ with a coproduct structure. We also obtain an evaluation homomorphism, that is, an algebra homomorphism from…

The affine Yangian of $\mathfrak{gl}_1$ is isomorphic to the universal enveloping algebra of $\mathcal{W}_{1+\infty}$ and can serve as a building block in the construction of new vertex operator algebras. In [1], a two-parameter family…

Young's lattice, the lattice of all Young diagrams, has the Robinson-Schensted-Knuth correspondence, the correspondence between certain matrices and pairs of semi-standard Young tableaux with the same shape. Fomin introduced generalized…

We extend to the super Yangian of the special linear Lie superalgebra $\mathfrak{sl}_{m|n}$ and its affine version certain results related to Schur-Weyl duality. We do the same for the deformed double current superalgebra of…

We find closed-form expressions for the Schur indices of 4d $\mathcal{N}=2^{*}$ super Yang-Mills theory with unitary gauge groups for arbitrary ranks via the Fermi-gas formulation. They can be written as a sum over the Young diagrams…

An attempt is described to extend the notion of Schur functions from Young diagrams to plane partitions. The suggestion is to use the recursion in the partition size, which is easily generalized and deformed. This opens a possibility to…

We continue the investigation of the central extended Yangian double [S. Khoroshkin, q-alg/9602031]. In this paper we study the intertwining operators for certain infinite dimensional representations of $\Yd$, which are deformed analogs of…

For affine special linear superalgebra $\widehat{sl}(m|n, \Pi)$ defined by an arbitrary system of simple roots $\Pi$ we define the affine super Yangian $Y_{\hbar}(\widehat{sl}(m|n, \Pi))$ as Hopf superalgebra which is a quantization of…

Recently, an intriguing correspondence was conjectured in arXiv:2409.11551 between Schur half-indices of pure 4d $SU(2)$ $\mathcal{N}=2$ supersymmetric Yang-Mills (SYM) theory with line operator insertions and partition functions of the…

Quasi-Yamanouchi tableaux are a subset of semistandard Young tableaux and refine standard Young tableaux. They are closely tied to the descent set of standard Young tableaux and were introduced by Assaf and Searles to tighten Gessel's…

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…

We show that the quantum Berezinian which gives a generating function of the integrals of motions of XXX spin chains associated to super Yangian $\mathrm{Y}(\mathfrak{gl}_{m|n})$ can be written as a ratio of two difference operators of…

We focus on the 1/4-BPS sector of free super Yang-Mills theory with an SO(N) gauge group. This theory has an AdS/CFT dual in the form of type IIB string theory with AdS_5 X RP^5 geometry. With the aim of studying excited giant graviton…

We study $\mathcal{N}=2$ superconformal field theory and define the R-matrix which acts as an intertwining operator between different realizations of $\mathcal{N}=2$ $W-$algebras of type $A$. Using this R-matrix we define $RLL$ algebra and…

The affine Yangian of $\mathfrak{gl}_1$ is known to be isomorphic to ${\cal W}_{1+\infty}$, the $W$-algebra that characterizes the bosonic higher spin -- CFT duality. In this paper we propose defining relations of the Yangian that are…

In this paper, we discuss the relations between the Jack polynomials, $\hbar$-dependent KP hierarchy and affine Yangian of ${\mathfrak{gl}}(1)$. We find that $\alpha=\hbar^2$ and $h_1=\hbar, \ h_2=-\hbar^{-1}$, where $\alpha$ is the…

Properties of the SO(2,n) Yangian acting on scalar and gauge fields are presented. This differential operator representation of the infinite-dimensional extension of the conformal algebra SO(2,n) is proved to satisfy the Serre relation for…