Introduction 185 5.3. Relating various algebras 220 1.1. Extensions of conformal symmetry 185 6. Quantum Drinfeld-Sokolov reduction 223 1.2. Studying extended symmetries 187 6.1. Introduction 223 1.3. Outline of the paper 189 6.2. Lagrange approach: constrained WZW and Toda field 2. Preliminaries 190 theories 223 2.1. Conformal invariance: basic notions 190 6.3. Algebraic approach to DS reduction 225 2.2. OPE's, normal ordered products and associativity 195 6.4. Representation theory 240 2.3. Auxiliary field theories 198 7. Coset constructions 244 3. 'W algebras and Casimir algebras 203 7.1. Introduction 244 3.1. V algebras: definitions and the example of~203 7.2. Casimir algebras 245 3.2. Casimir algebras 207 7.3. G X GIG coset conformal field theories 252 3.3. V superalgebras; the example of super-V 3 208 7.4. Other cosets 257 4. V algebras and CFI' 210 8. Further developments 260 4.1. The chiral algebra in RCFT's 210 8.1. V gravity 260 4.2. Examples: V~and super-V3 minimal models 212 8.2. V symmetry in string theory 263 5. Classification through direct construction 214 Appendix A. Lie algebra conventions 266 5.1. The method 214 Appendix B. V algebra nomenclature 267 5.2. Overview of results 215 References 268

No abstract

We present analytic and numerical calculations on the bipartite entanglement entropy in fractional quantum Hall states of the fermionic Laughlin sequence. The partitioning of the system is done both by dividing Landau-level orbitals and by grouping the fermions themselves. For the case of orbital partitioning, our results can be related to spatial partitioning, enabling us to extract a topological quantity (the "total quantum dimension") characterizing the Laughlin states. For particle partitioning we prove a very close upper bound for the entanglement entropy of a subset of the particles with the rest, and provide an interpretation in terms of exclusion statistics.