Quantum Group and $q$-Virasoro Current in Fermion Systems

TL;DR

This paper explores the extension of quantum groups to the q-Virasoro algebra in 2D electron systems under magnetic fields, revealing algebraic reductions and proposing a quantum group current model analogous to Hall current.

Contribution

It introduces a generalized quantum group framework for 2D electron systems and connects it to the q-Virasoro algebra, providing new insights into algebraic structures and current models.

Findings

Integral representations reduce to (1+1)-dimensional fermion forms

Quantum group symmetry enables a new current model

Analogous to Hall current in quantum group context

Abstract

We discuss a generalization of the quantum group $\su$ to the $q$-Virasoro algebra in two-dimensional electrons system under uniform magnetic field. It is shown that the integral representations of both algebras are reduced to those in a (1+1)-dimensional fermion. As an application of the quantum group symmetry, we discuss a model of quantum group current on the analogy of the Hall current.