q-differential operator representation of the quantum superalgebra Uq(sl(M+1|N+1))

TL;DR

This paper constructs a representation of the quantum superalgebra Uq(sl(M+1|N+1)) using q-differential operators on coherent states, facilitating the development of free field realizations for quantum affine superalgebras.

Contribution

It introduces a novel q-differential operator representation of Uq(sl(M+1|N+1)) based on coherent states, aiding in free field realization construction.

Findings

Representation based on q-differential operators on coherent states.

Provides a method to construct free field realizations for quantum affine superalgebras.

Connects local coordinates on flag manifolds to algebra representations.

Abstract

A representation of the quantum superalgebra Uq(sl(M+1|N+1)) is constructed based on the q-differential operators acting on the coherent states parameterized by coordinates. These coordinates correspond to the local ones of the flag manifold. This realization provides us with a guide to construct the free field realization for the quantum affine superalgebra Uq^(sl(M+1|N+1)) at arbitrary level.