Related papers: Principal W-algebras for GL(m|n)
The most general large ${\cal N}=4$ superconformal ${\cal W}_{\infty}$ algebra, containing in addition to the superconformal algebra one supermultiplet for each integer spin, is analysed in detail. It is found that the ${\cal W}_{\infty}$…
The Lie superalgebra $W(\infty)$ is defined to be the direct limit of the simple finite-dimensional Cartan type Lie superalgebras $W(n)$ as $n$ goes to infinity, where $W(n)$ denotes the Lie superalgebra of superderivations of the Grassmann…
Many $W$-algebras (e.g. the $W_N$ algebras) are consistent for all values of the central charge except for a discrete set of exceptional values. We show that such algebras can be contracted to new consistent degenerate algebras at these…
In this paper we construct resolutions of finite dimensional irreducible gl(m|n)-modules in terms of generalized Verma modules. The resolutions are determined by the Kostant cohomology groups and extend the strong…
In order to extend the geometrization of Yangian $R$-matrices from Lie algebras $gl(n)$ to superalgebras $gl(M|N)$, we introduce new quiver-related varieties which are associated with representations of $gl(M|N)$. In order to define them…
Let $k$ be an algebraically closed field of characteristic $p > 0$ and let $G$ be a connected reductive algebraic group over $k$. Under some standard hypothesis on $G$, we give a direct approach to the finite $W$-algebra $U(\mathfrak g,e)$…
We study the orbits and polynomial invariants of certain affine action of the super Weyl groupoid of Lie superalgebra $\mathfrak {gl}(n,m)$, depending on a parameter. We show that for generic values of the parameter all the orbits are…
The Yangian of the Lie algebra $gl_N$ has a distinguished family of irreducible finite-dimensional representations, called elementary representations. They are parametrized by pairs, consisting of a skew Young diagram and a complex number.…
$N=1$ supersymmetric gauge theories with global flavor symmetries contain a gauge invariant W-superalgebra which acts on its moduli space of gauge invariants. With adjoint matter, this superalgebra reduces to a graded Lie algebra. When the…
For each of the classical Lie algebras $g(n)=o(2n+1), sp(2n), o(2n)$ of type B, C, D we consider the centralizer of the subalgebra $g(n-m)$ in the universal enveloping algebra $U(g(n))$. We show that the $n$th centralizer algebra can be…
This paper is the detailed version of math.QA/0403477 (T. Arakawa, Quantized Reductions and Irreducible Representations of W-Algebras) with extended results; We study the representation theory of the W-algebra $W_k(g)$ associated with a…
It was recently shown that gl^(1|1) admits an infinite family of simple current extensions. Here, these findings are reviewed and explicit free field realisations of the extended algebras are constructed. The leading contributions to the…
We prove several basic properties of the Yangian of the general linear Lie superalgebra.
We construct a family of twisted generalized Weyl algebras which includes Weyl-Clifford superalgebras and quotients of the enveloping algebras of $\mathfrak{gl}(m|n)$ and $\mathfrak{osp}(m|2n)$. We give a condition for when a canonical…
We study analogues of the Yangian of the Lie algebra $gl_N$ for the other classical Lie algebras $so_N$ and $sp_N$. We call them twisted Yangians. They are coideal subalgebras in the Yangian $Y(gl_N)$ of $gl_N$ and admit homomorphisms onto…
We construct a new family of affine $W$-algebras $W^k(\lambda,\mu)$ parameterized by partitions $\lambda$ and $\mu$ associated with the centralizers of nilpotent elements in $\mathfrak{gl}_N$. The new family unifies a few known classes of…
Explicit expressions for the generators of the quantum superalgebra $U_q[gl(n/m)]$ acting on a class of irreducible representations are given. The class under consideration consists of all essentially typical representations: for these a…
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…
A three-parametric $R$-matrix satisfying a graded Yang-Baxter equation is introduced.This $R$-matrix allows us to construct new quantum supergroups which are deformations of the supergroup $GL(1/1)$ and the universal enveloping algebra…
We construct four edge contractions for the affine super Yangian of type $A$. By using these edge contractions, we give a homomorphism from the affine super Yangian of type $A$ to the universal enveloping algebra of the non-rectangular…