Universal factorization algebras of polynomials represent Lie algebras of endomorphisms

Abstract

The goal of this paper is to supply an explicit description of the universal factorization algebra of the generic polynomial of degree [Formula: see text] into the product of two monic polynomials, one of degree [Formula: see text], as a representation of Lie algebras of [Formula: see text] matrices with polynomial entries. This is related with the bosonic vertex representation of the Lie algebra [Formula: see text] due to Date, Jimbo, Kashiwara and Miwa.