相关论文: Classical W-algebras for gl_N and associated integ…
In this paper we present a systematic study of $W$ algebras from the Hamiltonian reduction point of view. The Drinfeld-Sokolov (DS) reduction scheme is generalized to arbitrary $sl_2$ embeddings thus showing that a large class of W algebras…
In this paper we study the variety of one dimensional representations of a finite $W$-algebra attached to a classical Lie algebra, giving a precise description of the dimensions of the irreducible components. We apply this to prove a…
For any connected complex reductive group $G$ and element $z$ of its Weyl group $W$, we use work of Lusztig and Abreu-Nigro to compute the graded $W$-character of the intersection cohomology of any closed Lusztig variety for $z$ over the…
Exploiting the residual gauge freedom in the formulation of constrained KP hierarchy a number of new integrable systems are derived including hierarchies of Kundu-Eckhaus equation and higher order nonlinear extensions of Yajima-Oikawa and…
We introduce linear Dirac and generalized complex structures on Cartan geometries and give criteria for Dirac subalgebras of $\frkg\ltimes\frkg^*$ representing Dirac structures on a Cartan geometry. We prove that there is a bijection…
In this paper we combine many of the standard and more recent algebraic techniques for testing isomorphism of finite groups (GpI) with combinatorial techniques that have typically been applied to Graph Isomorphism. In particular, we show…
We present a formula for a classical $r$-matrix of an integrable system obtained by Hamiltonian reduction of some free field theories using pure gauge symmetries. The framework of the reduction is restricted only by the assumption that the…
It is proved that for a vector space W, any set of parafermion-like vertex operators on W in a certain canonical way generates a generalized vertex algebra in the sense of [DL2] with W as a natural module. This result generalizes a result…
We introduce a generalisation of the KP hierarchy, closely related to the cyclic quiver and the Cherednik algebra $H_k(\mathbb Z_m)$. This hierarchy depends on $m$ parameters (one of which can be eliminated), with the usual KP hierarchy…
Wawamoto generalized the Witt algebra using Laurent extension of polynomial ring. We construct the generalized Witt algebra $W(g_p,n)$ by using an additive map $g_p$ from a set of integers into a field of characteristic zero where $1\leq p…
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…
This paper shows that the Ablowitz-Ladik hierarchy of equations (a well-known integrable discretization of the Non-linear Schrodinger system) can be explicitly viewed as a hierarchy of commuting flows which: (a) are Hamiltonian with respect…
Finite rational $\cw$ algebras are very natural structures appearing in coset constructions when a Kac-Moody subalgebra is factored out. In this letter we address the problem of relating these algebras to integrable hierarchies of…
We show that the bi-Hamiltonian structures of the Camassa-Holm and Harry Dym hierarchies can be obtained by applying a reduction process to a simple Poisson pair defined on the loop algebra of $\mathfrak{sl}(2,\mathbb{R})$. The reduction…
We present a general framework for constructing polynomial integrable systems on linearizations of Poisson varieties that admit log-canonical systems. Our construction is in particular applicable to Poisson varieties with compatible cluster…
In a recent paper, the authors have shown that the secondary reduction of W-algebras provides a natural framework for the linearization of W-algebras. In particular, it allows in a very simple way the calculation of the linear algebra…
We consider the integrable Camassa--Holm hierarchy on the line with positive initial data rapidly decaying at infinity. It is known that flows of the hierarchy can be formulated in a Hamiltonian form using two compatible Poisson brackets.…
We introduce a family of compatible Poisson brackets on the space of $2\times 2$ polynomial matrices, which contains the reflection equation algebra bracket. Then we use it to derive a multi-Hamiltonian structure for a set of integrable…
We propose a consistently algebraic formulation of the extended KP (supersymmetric) integrable -hierarchy systems. We exploit the results already established in [14] and which consist in a framework suspected to unify in a fascinating way…
Given a finite-dimensional complex Lie algebra g equipped with a nondegenerate, symmetric, invariant bilinear form B, let V_k(g,B) denote the universal affine vertex algebra associated to g and B at level k. For any reductive group G of…