Related papers: Quantized symplectic actions and W-algebras

In this paper we construct finite dimensional representations of the wreath product symplectic reflection algebra H(k,c,N,G) of rank N attached to a finite subgroup G of SL(2,C) (here k is a number and c a class function on the set of…

Let $\mathfrak g$ be a complex reductive Lie algebra and $V$ the underling vector space of a finite-dimensional representation of $\mathfrak g$. Then one can consider a new Lie algebra $\mathfrak q=\mathfrak g{\ltimes} V$, which is a…

We formulate and prove examples of a conjecture which describes the W-algebras in type A as successive quantum Hamiltonian reductions of affine vertex algebras associated with several hook-type nilpotent orbits. This implies that the affine…

The property of some finite W-algebras to appear as the commutant of a particular subalgebra in a simple Lie algebra G is exploited for the obtention of new G-realizations from a "canonical" differential one. The method is applied to the…

We introduce a new family of Poisson vertex algebras $\mathcal{W}(\mathfrak{a})$ analogous to the classical $\mathcal{W}$-algebras. The algebra $\mathcal{W}(\mathfrak{a})$ is associated with the centralizer $\mathfrak{a}$ of an arbitrary…

A finite $W$-algebra $U(\g,e)$ is a certain finitely generated algebra that can be viewed as the enveloping algebra of the Slodowy slice to the adjoint orbit of a nilpotent element $e$ of a complex reductive Lie algebra $\g$. It is possible…

The equivariant $\mathcal{W}$-algebra of a simple Lie algebra $\mathfrak{g}$ is a BRST reduction of the algebra of chiral differential operators on the Lie group of $\mathfrak{g}$. We construct a family of vertex algebras $A[\mathfrak{g},…

The ``local'' structure of a quantum group G_q is currently considered to be an infinite-dimensional object: the corresponding quantum universal enveloping algebra U_q(g), which is a Hopf algebra deformation of the universal enveloping…

We present a classification of $W$ algebras and superalgebras arising in Abelian as well as non Abelian Toda theories. Each model, obtained from a constrained WZW action, is related with an $Sl(2)$ subalgebra (resp. $OSp(1|2)$ superalgebra)…

For a finite dimensional semisimple Lie algebra ${\frak{g}}$ and a root $q$ of unity in a field $k,$ we associate to these data a double quiver $\bar{\cal{Q}}.$ It is shown that a restricted version of the quantized enveloping algebras…

We consider the natural Lie algebra structure on the (associative) group algebra of a finite group $G$, and show that the Lie subalgebras associated to natural involutive antiautomorphisms of this group algebra are reductive ones. We give a…

We re-examine some topics in representation theory of Lie algebras and Springer theory in a more general context, viewing the universal enveloping algebra as an example of the section ring of a quantization of a conical symplectic…

We classify all the pairs of a commutative associative algebra with an identity element and its finite-dimensional commutative locally-finite derivation subalgebra such that the commutative associative algebra is derivation-simple with…

In this paper we study the finite W-algebra for the queer Lie superalgebra Q(n) associated with the non-regular even nilpotent coadjoint orbits in the case when the corresponding nilpotent element has Jordan blocks each of size l. We prove…

We show there is a class of symplectic Lie algebra representations over any field of characteristic not 2 or 3 that have many of the exceptional algebraic and geometric properties of both symmetric three forms in two dimensions and…

Let G be a connected reductive group acting on a finite dimensional vector space V. Assume that V is equipped with a G-invariant symplectic form. Then the ring C[V] of polynomial functions becomes a Poisson algebra. The ring C[V]^G of…

Let $\mathfrak{g}$ be a semi-simple Lie algebra with fixed root system, and $U_q(\mathfrak{g})$ the quantization of its universal enveloping algebra. Let $\mathcal{S}$ be a subset of the simple roots of $\mathfrak{g}$. We show that the…

We propose a novel quantum integrable model for every non-simply laced simple Lie algebra ${\mathfrak g}$, which we call the folded integrable model. Its spectra correspond to solutions of the Bethe Ansatz equations obtained by folding the…

We introduce a new family of affine $W$-algebras associated with the centralizers of arbitrary nilpotent elements in $\mathfrak{gl}_N$. We define them by using a version of the BRST complex of the quantum Drinfeld--Sokolov reduction. A…

We propose a series of new subalgebras of the $W_{1+\infty}$ algebra parametrized by polynomials $p(w)$, and study their quasifinite representations. We also investigate the relation between such subalgebras and the…