Algebraic classical $W$-algebras and Frobenius manifolds

Yassir Ibrahim Dinar

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arXiv · 1911.00271

Algebraic classical $W$-algebras and Frobenius manifolds

Yassir Ibrahim Dinar

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Abstract

We consider Drinfeld-Sokolov bihamiltonian structure associated to 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 form 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.

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BibTeX RIS

Yassir Ibrahim Dinar. 2019-11-01. Algebraic classical $W$-algebras and Frobenius manifolds. https://arxiv.org/abs/1911.00271

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