Elliptic Deformed Superalgebra $u_{q,p}(\hat{{sl}}(M|N))$

TL;DR

This paper introduces a new elliptic superalgebra as a one-parameter deformation of the quantum superalgebra, providing explicit bosonization and screening currents for a specific case at arbitrary levels.

Contribution

It presents the first bosonization of the elliptic superalgebra $U_{q,p}( ext{hat} sl(1|2))$ and constructs screening currents that commute with it.

Findings

Bosonization of $U_{q,p}( ext{hat} sl(1|2))$ for arbitrary level $k eq 1$

Construction of screening currents commuting with the elliptic superalgebra

Extension of quantum superalgebra to elliptic deformation

Abstract

We introduce the elliptic superalgebra $U_{q,p}(\hat{sl}(M|N))$ as one parameter deformation of the quantum superalgebra $U_q(\hat{sl}(M|N))$. For an arbitrary level $k \neq 1$ we give the bosonization of the elliptic superalgebra $U_{q,p}(\hat{sl}(1|2))$ and the screening currents that commute with $U_{q,p}(\hat{sl}(1|2))$ modulo total difference.