Free field realization of commutative family of elliptic Feigin-Odesskii algebra

TL;DR

This paper reviews the free field realizations of the Feigin-Odesskii algebra, constructing a pair of infinitely many commutative operators linked to the elliptic quantum group U_{q,p}(\,sl_N).

Contribution

It introduces a new free field realization of a commutative family of operators associated with elliptic quantum groups.

Findings

Constructed free field realizations of commutative operators

Linked these operators to elliptic quantum groups

Enhanced understanding of algebraic structures in quantum groups

Abstract

In this review, we study free field realizations of the Feigin-Odesskii algebra. We construct free field realizations of a pair of infinitely many commutative operators, associated with the elliptic quantum group $U_{q,p}(\widehat{sl_N})$.