From AGD Brackets to Logarithmic Frobenius Manifolds

Yassir Dinar (Sultan Qaboos University)

Tuesday 27th May 16:00-17:00
Maths 311B

Abstract

We explore the construction of a local Poisson bracket compatible with the second Adler-Gelfand-Dickey (AGD) bracket, yielding a bihamiltonian structure distinct from the classical Drinfeld-Sokolov framework. The dispersionless limit of this new structure gives rise to logarithmic Dubrovin-Frobenius manifold structures on the orbit spaces associated with the standard representation of the symmetric group. In low dimensions, we demonstrate that the resulting bihamiltonian structure is equivalent—via generalized Miura-type transformations—to the one associated with the constrained KP hierarchy.

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