262 citations · 3.5k across the 155 of their papers we have counts for
48 papers · 1 filter
Poisson vertex algebras and Hamiltonian PDE
Alberto De Sole, Victor G. Kac, Daniele Valeri
We discuss the theory of Poisson vertex algebras and their generalizations in relation to integrability of Hamiltonian PDE. In particular, we discuss the theory of affine classical…
Multicomponent KP type hierarchies and their reductions, associated to conjugacy classes of Weyl groups of classical Lie algebras
Victor Kac, Johan van de Leur
This, to a large extent, expository paper, describes the theory of multicomponent hierarchies of evolution equations of XKP type, where X=A, B, C or D, and AKP=KP, and their reduct…
The generalized Giambelli formula and polynomial KP and CKP tau-functions
Victor Kac, Johan van de Leur
The first part of the paper is devoted to two descriptions of all polynomial tau-functions of the KP hierarchy: by a generalized Jacobi-Trudy formula, and a generalized Giambelli f…
Integrability of classical affine W-algebras
Alberto De Sole, Mamuka Jibladze, Victor G. Kac +1
We prove that all classical affine W-algebras W(g,f), where g is a simple Lie algebra and f is its non-zero nilpotent element, admit an integrable hierarchy of bi-Hamiltonian PDEs,…
p-reduced multicomponent KP hierarchy and classical W-algebras W(gl_N,p)
Sylvain Carpentier, Alberto De Sole, Victor G. Kac +2
For each partition p of an integer N \geq 2, consisting of r parts, an integrable hierarchy of Lax type Hamiltonian PDE has been constructed recently by some of us. In the present…
Polynomial tau-functions for the multi-component KP hierarchy
Victor Kac, Johan van de Leur
In a previous paper we constructed all polynomial tau-functions of the 1-component KP hierarchy, namely, we showed that any such tau-function is obtained from a Schur polynomial $s…