Related papers: Gelfand-Tsetlin varieties for Yangians
Let $E/F$ be a quadratic extension of non-Archimedean local fields of characteristic 0. Let $D$ be the unique quaternion division algebra over $F$ and fix an embedding of $E$ to $D$. Then, $\mathrm{GL}_m(D)$ can be regarded as a subgroup of…
An action of the Yangian of the general Lie algebra gl(N) is defined on every irreducible integrable highest weight module of affine gl(N) with level greater than 1. This action is derived, by means of the Drinfeld duality and a subsequent…
We present a self-contained formulation of the Nonlinear Schrodinger hierarchy and its Yangian symmetry in terms of deformed oscilator algebra (Z.F. algebra). The link between Yangian Y(gl(N)) and finite W(gl(pN),N.gl(p)) algebras is also…
In third paper of the series we construct a large family of representations of the quantum toroidal $\gl_1$ algebra whose bases are parameterized by plane partitions with various boundary conditions and restrictions. We study the…
We discuss the generalized Yang Poisson models. We construct generalizations of the Yang Poisson algebra related to $\mathfrak{o}(1,5)$ algebra discussed by Meljanac and Mignemi (2023). The exact realizations of this generalized algebra on…
We provide a classification and an explicit realization of all irreducible Gelfand-Tsetlin modules of the complex Lie algebra sl(3). The realization of these modules uses regular and derivative Gelfand-Tsetlin tableaux. In particular, we…
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…
On the basis of graded RTT formalism,the defining relation of the super-Yangian Y(gl(1|1)) is derived and its oscillator realization is constructed.
New commutative subalgebras of the maximal Gel'fand-Kirillov dimension in the universal enveloping algebras of classical Lie algebras gl(n) and so(n) are constructed. In the case of sp(n) Gel'fand-Tsetlin algebra is extended to a maximally…
In the paper using the method of $Z$-invariants of Zhelobenko we construct base vectors of Gelfand-Tsetlin type in a representation of $\mathfrak{o}_{2n+1}$, based on restrictions $\mathfrak{o}_{2n+1}\downarrow\mathfrak{o}_{2n-1}$. The…
We construct a groupoid equivariant Kasparov class for transversely oriented foliations in all codimensions. In codimension 1 we show that the Chern character of an associated semifinite spectral triple recovers the Connes-Moscovici cyclic…
Let $d$ be a positive integer. The Yangian $Y_d=Y(\mathfrak{gl}(d,\mathbb C))$ of the general linear Lie algebra $\mathfrak{gl}(d,\mathbb C)$ has countably many generators and quadratic-linear defining relations, which can be packed into a…
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.
We prove that every pre-Nichols algebra of a nondiagonal object in the twisted Yetter-Drinfeld category ${_{\k G}^{\k G} {\mathcal{YD}^\Phi}}$ has infinite Gelfand-Kirillov dimension, where $G$ is a finite abelian group and $\Phi$ is a…
We define the super Yangian $Y_{m|n}$ over a field $\mathbbm{k}$ of characteristic $2$, and show that the super Yangian $Y_{m|n}$ is a deformation of the super universal enveloping algebra of the current Lie algebra…
We study a certain type of multiple commutation relations of the quantum affine algebra $U_q(\widehat{\mathfrak{gl}}_N)$. We show that all the coefficients in the multiple commutation relations between the $L$-operator elements are given in…
In this note, we generalize the notion of quantum Berezinian to the double Yangian ${\rm DY}(\mathfrak{gl}_{m|n})$ of the Lie superalgebra $\mathfrak{gl}_{m|n}$. We show that its coefficients form a family of algebraically independent…
We prove a uniqueness theorem for irreducible non-critical Gelfand-Tsetlin modules. The uniqueness result leads to a complete classification of the irreducible Gelfand-Tsetlin modules with 1-singularity. An explicit construction of such…
Yetter--Drinfel'd modules of diagonal type admit an equivalence relation which conjecturally preserves dimension and Gel'fand--Kirillov dimension of the corresponding Nichols algebras. This relation is determined explicitly for all rank 2…
We introduce nonabelian analogs of shift operators in the enumerative theory of quasimaps. We apply them on the one hand to strengthen the emerging analogy between enumerative geometry and the geometric theory of automorphic forms, and on…