Related papers: Building blocks for $W$-algebras of classical type…

The four different kinds of currents are given by the multiple $(\beta,\gamma)$ and $(b,c)$ ghost systems with a multiple product of derivatives. We determine their complete algebra where the structure constants depend on the deformation…

This is a paper in a series to study vertex algebra-like structures arising from various algebras including quantum affine algebras and Yangians. In this paper, we study notions of $\hbar$-adic nonlocal vertex algebra and $\hbar$-adic…

String diagrams turn algebraic equations into topological moves that have recurring shapes, involving the sliding of one diagram past another. We individuate, at the root of this fact, the dual nature of polygraphs as presentations of…

This paper introduces and systematically studies a new class of non-commutative algebras -- Weyl-type and Witt-type algebras -- generated by differential operators with exponential and generalized power function coefficients. We define the…

We construct the classical W-algebras for some non-abelian Toda systems associated with the Lie groups GL(2n,R) and Sp(n,R). We start with the set of characteristic integrals and find the Poisson brackets for the corresponding Hamiltonian…

Within the framework of the discrete Wess-Zumino-Novikov-Witten theory we analyze the structure of vertex operators on a lattice. In particular, the lattice analogues of operator product expansions and braid relations are discussed. As the…

We define a theory of parameterized algebraic complexity classes in analogy to parameterized Boolean counting classes. We define the classes VFPT and VW[t], which mirror the Boolean counting classes #FPT and #W[t], and define appropriate…

The Weyl algebra (W_{2m}[h]; *) is the algebra generated by u=(u_1,...,u_m,v_1,.....,v_m) over C with the fundamental commutation relation [u_i,v_j]=-ih\delta_{ij}, where h is a positive constant. The Heisenberg algebra (\Cal H_{2m}[nu];*)…

We study parafermion vertex algebras $N_{-3/2}(\frak{sl}(2))$ and $N_{-3/2}(\frak{sl}(3))$. Using the isomorphism between $N_{-3/2}(\frak{sl}(3))$ and the logarithmic vertex algebra $\mathcal{W}^{0} (2)_{A_2} $ from [2], we show that these…

A proposal for constructing a universal nonlinear ${\hat W}_{\infty}$ algebra is made as the symmetry algebra of a rotational Killing-symmetry reduction of the nonlinear perturbations of Moyal-Integrable deformations of $D=4$ Self Dual…

We introduce a family of unital associative algebras A which are multiparameter analogues of the Weyl algebras and determine the simple weight modules and the Whittaker modules for them. All these modules can be regarded as spaces of…

We represent Feigin's construction [11] of lattice W algebras and give some simple results: lattice Virasoro and $W_3$ algebras. For simplest case $g=sl(2)$ we introduce whole $U_q(sl(2))$ quantum group on this lattice. We find simplest…

We study a family of integrals parameterised by $ N = 2,3,\dots $ generalising the Askey-Wilson integral $ N=2 $ which has arisen in the theory of $q$-analogs of monodromy preserving deformations of linear differential systems and in theory…

For the algebraic group $SL_{l+1}(\mathbb{C})$ we describe a system of positive roots associated to conjugacy classes in its Weyl group. Using this we explicitly describe the algebra of regular functions on certain transverse slices to…

For coprime $p,q\in\mathbb{Z}_{\geq 2}$, the triplet vertex operator algebra $W_{p,q}$ is a non-simple extension of the universal Virasoro vertex operator algebra of central charge $c_{p,q}=1-\frac{6(p-q)^2}{pq}$, and it is a basic example…

Let W -> A^2 be the universal Weierstrass family of cubic curves over C. For each N >= 2, we construct surfaces parametrizing the three standard kinds of level N structures on the smooth fibers of W. We then complete these surfaces to…

In this paper, W*-algebras are presented as canonical colimits of diagrams of matrix algebras and completely positive maps. In other words, matrix algebras are dense in W*-algebras.

We construct a family of potentially quasi-lisse (non-rational) vertex algebras, denoted by $\mathcal{C}_p$, $p \geq 2$, which are closely related to the vertex algebra of chiral differential operators on $SL(2)$ at level $-2+\frac{1}{p}$.…

For any $\mathbf{a}=(a_1,\dots,a_n)\in \mathbb{C}^n$, we introduce a Whittaker category $\mathcal{H}_{\mathbf{a}}$ whose objects are $\mathfrak{sl}_{n+1}$-modules $M$ such that $e_{0i}-a_i$ acts locally nilpotently on $M$ for all $i \in…

The Jucys-Murphy elements for wreath products G_n associated to any finite group G are introduced and they play an important role in our study on the connections between class algebras of G_n for all n and vertex algebras. We construct an…