Abstract
We consider Drinfeld–Sokolov bihamiltonian structure associated with a distinguished nilpotent elements of semisimple type and the space of common equilibrium points defined by its leading term. On this space, we construct a local bihamiltonian structure which forms an exact Poisson pencil, defines an algebraic classical W-algebra, admits a dispersionless limit, and its leading term defines an algebraic Frobenius manifold. This leads to a uniform construction of algebraic Frobenius manifolds corresponding to regular cuspidal conjugacy classes in irreducible Weyl groups.
Original language | English |
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Article number | 115 |
Journal | Letters in Mathematical Physics |
Volume | 111 |
Issue number | 5 |
DOIs | |
Publication status | Published - Oct 2021 |
Keywords
- Classical W-algebra
- Common equilibrium points
- Drinfeld–Sokolov reduction
- Exact Poisson pencil
- Frobenius manifolds
- Nilpotent orbits in Lie algebras
ASJC Scopus subject areas
- Statistical and Nonlinear Physics
- Mathematical Physics