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.
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Research Article| March 06 2018
Singular vectors for the WN algebras
David Ridout, Steve Siu, Simon Wood; Singular vectors for the WN algebras. J. Math. Phys. 1 March 2018; 59 (3): 031701. https://doi.org/10.1063/1.5019278
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