Finite W-algebras and intermediate statistics Original Research Article

New realizations of finite W-algebras are constructed by relaxing the usual constraint conditions. Then finite W-algebras are recognized in the Heisenberg quantization recently proposed by Leinaas and Myrheim, for a system of two identical particles in d dimensions. As the anyonic parameter is directly associated to the W-algebra involved in the d = 1 case, it is natural to consider that the W-algebra framework is well adapted for a possible generalization of the anyon statistics.