An analog of the Feigin-Frenkel homomorphism for double loop algebras

TL;DR

This paper constructs a vertex algebra homomorphism for double loop algebras, extending the Feigin-Frenkel homomorphism concept from affine algebras to a more complex setting.

Contribution

It introduces a novel homomorphism of vertex algebras for double loop algebras, inspired by the Feigin-Frenkel construction for affine algebras.

Findings

Established the existence of the homomorphism

Extended Feigin-Frenkel framework to double loop algebras

Provided a new algebraic structure for double loop algebras

Abstract

We prove the existence of a homomorphism of vertex algebras, from the vacuum Verma module over the loop algebra of an untwisted affine algebra, whose construction is analogous to that of the Feigin-Frenkel homomorphism from the vacuum Verma module at critical level over an affine algebra.