Classification of Quantum Hall Universality Classes by $W_{1+\infty }$ symmetry

Abstract

We show how two-dimensional incompressible quantum fluids and their excitations can be viewed as $W_{1+\infty }$ edge conformal field theories, thereby providing an algebraic characterization of incompressibility. The Kac-Radul representation theory of the $W_{1+\infty }$ algebra leads then to a purely algebraic complete classification of hierarchical quantum Hall states, which encompasses all measured fractions. Spin-polarized electrons in single-layer devices can only have Abelian anyon excitations.

11 pages, RevTeX 3.0, MPI-Ph/93-75 DFTT 65/93

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