In this seminar I will report about an ongoing research with D. Valeri. It is known that classical affine Walgebras arise from a generalized DrinfeldSokolov reduction of a simple Lie algebra. Using the language of Poisson Vertex Algebra we are able to perform such reduction for any simple Lie algebra and nilpotent orbit, with limited computational effort. As already observed by O. Pavlyk and Y. Dinar for the D4 subregular case, the biHamiltonian structures of classical Walgebras do not admit a dispersionless limit when the reduction has been obtained from any but the principal nilpotent orbit. A suitable Dirac reduction, however, allows to perform the limit and to obtain a biHamiltonian pencil of hydrodynamic type. I will present Pavlyk and Dinar examples, as well as some new ones obtained by A type Lie algebras.
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Dispersionless limit for the biHamiltonian structure of classical affine Walgebras
Research Group:
Matteo Casati
Institution:
Università di Bergamo
Location:
A136
Schedule:
Wednesday, May 4, 2016  14:30
Abstract:
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