In this paper, we use free field realisations of the A-type principal, or Casimir, WN algebras to derive explicit formulae for singular vectors in Fock modules. These singular vectors are constructed by applying screening operators to Fock module highest weight vectors. The action of the screening operators is then explicitly evaluated in terms of Jack symmetric functions and their skew analogues. The resulting formulae depend on sequences of pairs of integers that completely determine the Fock module as well as the Jack symmetric functions.

Topics
Covariant formulation, Lie algebras, Algebraic structures, Group theory, Symmetry functions, Representation theory, Functions and mappings, Conformal field theory, Hilbert space, Operator product expansion
© 2018 Author(s).
2018
Author(s)
You do not currently have access to this content.