Frobenius manifolds from subregular classical $W$-algebras

TL;DR

This paper constructs algebraic Frobenius manifolds from classical W-algebras linked to subregular nilpotent elements in specific Lie algebras, connecting them to hypersurface singularities and their deformations.

Contribution

It introduces a novel method to derive Frobenius manifolds from classical W-algebras associated with subregular nilpotent elements in Lie algebras of types D and E.

Findings

Frobenius manifolds are realized as hypersurfaces in deformation spaces

Establishes a link between W-algebras and hypersurface singularities

Provides explicit algebraic structures for these Frobenius manifolds

Abstract

We obtain algebraic Frobenius manifolds from classical $W$-algebras associated to subregular nilpotent elements in simple Lie algebras of type $D_r$ where $r$ is even and $E_r$. The resulting Frobenius manifolds are certain hypersurfaces in the total spaces of semiuniversal deformation of simple hypersurface singularities of the same types.