262 citations · 3.5k across the 155 of their papers we have counts for
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Double Poisson vertex algebras and non-commutative Hamiltonian equations
Alberto De Sole, Victor G. Kac, Daniele Valeri
We develop the formalism of double Poisson vertex algebras (local and non-local) aimed at the study of non-commutative Hamiltionan PDEs. This is a generalization of the theory of d…
Characters of (relatively) integrable modules over affine Lie superlagebras
Maria Gorelik, Victor Kac
In the paper we consider the problem of computation of characters of relatively integrable irreducible highest weight modules over finite-dimensional basic Lie superalgebras an…
On integrability of some bi-Hamiltonian two field systems of PDE
Alberto De Sole, Victor G. Kac, Refik Turhan
We continue the study of integrability of bi-Hamiltonian systems with a compatible pair of local Poisson structures (H_0,H_1), where H_0 is a strongly skew-adjoint operator. This i…
Structure of classical (finite and affine) W-algebras
Alberto De Sole, Victor G. Kac, Daniele Valeri
First, we derive an explicit formula for the Poisson bracket of the classical finite W-algebra W^{fin}(g,f), the algebra of polynomial functions on the Slodowy slice associated to…
Representations of affine superalgebras and mock theta functions II
Victor G. Kac, Minoru Wakimoto
We show that the normalized supercharacters of principal admissible modules, associated to each integrable atypical module over the affine Lie superalgebra can…
Adler-Gelfand-Dickey approach to classical W-algebras within the theory of Poisson vertex algebras
Alberto De Sole, Victor G. Kac, Daniele Valeri
We put the Adler-Gelfand-Dickey approach to classical W-algebras in the framework of Poisson vertex algebras. We show how to recover the bi-Poisson structure of the KP hierarchy, t…