Classical affine \(\mathcal{W}\)-algebras for \(\mathfrak{gl}_N\) and associated integrable Hamiltonian hierarchies
DOI10.1007/s00220-016-2632-9zbMath1433.17038arXiv1509.06878OpenAlexW3121783259MaRDI QIDQ329597
Victor G. Kac, Daniele Valeri, Alberto De Sole
Publication date: 21 October 2016
Published in: Communications in Mathematical Physics (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1509.06878
Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Vertex operators; vertex operator algebras and related structures (17B69) Applications of Lie algebras and superalgebras to integrable systems (17B80) Relations of infinite-dimensional Hamiltonian and Lagrangian dynamical systems with infinite-dimensional Lie algebras and other algebraic structures (37K30)
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Cites Work
- Unnamed Item
- Structure of classical (finite and affine) \(\mathcal W\)-algebras
- A new scheme of integrability for (bi)Hamiltonian PDE
- Non-local Poisson structures and applications to the theory of integrable systems
- Classical \(\mathcal W\)-algebras and generalized Drinfeld-Sokolov bi-Hamiltonian systems within the theory of Poisson vertex algebras
- Dirac reduction for Poisson vertex algebras
- Classical \(\mathcal{W}\)-algebras and generalized Drinfeld-Sokolov hierarchies for minimal and short nilpotents
- Finite vs affine \(W\)-algebras
- Lie algebras and equations of Korteweg-de Vries type
- The resonant interaction among long and short waves
- Generalized Drinfel'd-Sokolov hierarchies
- Fractional powers of operators and Hamiltonian systems
- On a trace functional for formal pseudo-differential operators and the symplectic structure of the Korteweg-deVries type equations
- Finite \(W\)-algebras for \(\mathfrak{gl}_N\)
- Quasideterminants
- Generalized Drinfeld-Sokolov reductions and KdV type hierarchies
- Generalized Drinfel'd-Sokolov hierarchies. II: The Hamiltonian structures
- \({\mathcal W}\)-algebras from soliton equations and Heisenberg subalgebras
- Classical \(\mathcal W\)-algebras in types \(A\), \(B\), \(C\), \(D\) and \(G\)
- Poisson vertex algebras in the theory of Hamiltonian equations
- Toda theory and \({\mathcal W}\)-algebra from a gauged WZNW point of view
- Erratum to: ``Classical \(\mathcal W\)-algebras and generalized Drinfeld-Sokolov hierarchies for minimal and short nilpotents
- Formation and Interaction of Sonic-Langmuir Solitons: Inverse Scattering Method
- Good grading polytopes
- Adler–Gelfand–Dickey Approach to Classical 𝒲-Algebras Within the Theory of Poisson Vertex Algebras
- New reductions of the Kadomtsev–Petviashvili and two-dimensional Toda lattice hierarchies via symmetry constraints
- Constraints of the Kadomtsev–Petviashvili hierarchy
- A simple model of the integrable Hamiltonian equation
- Multicomponent integrable reductions in the Kadomtsev–Petviashvilli hierarchy
- Solutions for the vector k-constrained KP hierarchy
- Regular conjugacy classes in the Weyl group and integrable hierarchies