Finite $W$-algebra invariants via Lax type operators

TL;DR

This paper develops explicit formulas for generators of finite W-algebras of types B, C, D with even Dynkin grading using Lax type operators, advancing understanding of their algebraic structure.

Contribution

It introduces a novel approach using Lax type operators to explicitly construct generators of finite W-algebras in specific types.

Findings

Explicit formulas for generators of finite W-algebras of types B, C, D

Complete set of generators for all such W-algebras with even Dynkin grading

Method extends to a broad class of finite W-algebras

Abstract

We use variations on Lax type operators to find explicit formulas for certain elements of finite $W$-algebras. These give a complete set of generators for all finite $W$-algebras of types B,C,D for which the Dynkin grading is even.