Frobenius manifolds from regular classical $W$-algebras

Abstract

We obtain polynomial Frobenius manifolds from classical $W$-algebras associated to regular nilpotent elements in simple Lie algebras using the related opposite Cartan subalgebras.

References in corpus (5)

• Normal forms of hierarchies of integrable PDEs, Frobenius manifolds and Gromov - Witten invariants
• Regular Conjugacy Classes in the Weyl Group and Integrable Hierarchies
• Differential geometry of the space of orbits of a Coxeter group
• On the Completeness of the Set of Classical W-Algebras Obtained from DS Reductions
• On classification and construction of algebraic Frobenius manifolds

Cited by in corpus (6)

• Classical $r$-matrix like approach to Frobenius manifolds, WDVV equations and flat metrics
• Hurwitz numbers for reflection groups II: Parabolic quasi-Coxeter elements
• The quadratic WDVV solution $E_8(a_1)$
• Weights of Semiregular Nilpotents in Simple Lie Algebras of D Type
• Conjugate Frobenius manifold and inversion symmetry
• $W$-algebras and the equivalence of bihamiltonian, Drinfeld-Sokolov and Dirac reductions