Bosonic realization of toroidal Lie algebras of classical types

TL;DR

This paper extends the bosonic realization framework to construct toroidal Lie algebras of classical types, providing new insights and methods for representing these complex algebraic structures.

Contribution

It introduces a generalized bosonic construction for toroidal Lie algebras of types A, B, C, D, including new representations for orthogonal Lie algebras.

Findings

Constructed toroidal Lie algebras of types A, B, C, D using Weyl bosonic fields.

Provided bosonic realizations for orthogonal Lie algebras in affine cases.

Achieved level-specific constructions for each algebra type.

Abstract

Generalizing Feingold-Frenkel's construction we use Weyl bosonic fields to construct toroidal Lie algebras of types $A_n, B_n$, $C_n$ and $D_n$ of level $-1, -2, -1/2$ and -2 respectively. In particular, our construction also gives new bosonic construction for the orthogonal Lie algebras in the cases of affine Lie algebras.