On the irreducibility of associated varieties of W-algebras

TL;DR

This paper studies the geometric structure of associated varieties of W-algebras, focusing on their irreducibility and the presence of finitely many symplectic leaves, contributing to the understanding of their algebraic and geometric properties.

Contribution

It establishes conditions for irreducibility of associated varieties and provides new examples of vertex algebras with finitely many symplectic leaves.

Findings

Irreducibility of certain nilpotent Slodowy slices analyzed.

New examples of vertex algebras with finitely many symplectic leaves provided.

Enhanced understanding of the geometric structure of W-algebras.

Abstract

We investigate the irreducibility of the nilpotent Slodowy slices that appear as the associated variety of W-algebras. Furthermore, we provide new examples of vertex algebras whose associated variety has finitely many symplectic leaves.