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We show how two-dimensional incompressible quantum fluids and theirexcitations can be viewed as $\ W_{1+\infty}\ $ edge conformal field theories,thereby providing an algebraic characterization of incompressibility. TheKac-Radul representation theory of the $\ W_{1+\infty}\ $ algebra leads then toa purely algebraic complete classification of hierarchical quantum Hall states,which encompasses all measured fractions. Spin-polarized electrons insingle-layer devices can only have Abelian anyon excitations.Comment: 11 pages, RevTeX 3.0, MPI-Ph/93-75 DFTT 65/9

physical review letters

Classification of quantum Hall universality classes by<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant="italic">W</mml:mi></mml:mrow><mml:mrow><mml:mn>1</mml:mn><mml:mo>+</mml:mo><mml:mi mathvariant="normal">∞</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math>symmetry

Classification of quantum Hall universality classes byW1+∞symmetry