Journal article
Singular vectors for the WN algebras
D Ridout, S Siu, S Wood
Journal of Mathematical Physics | AMER INST PHYSICS | Published : 2018
DOI: 10.1063/1.5019278
Abstract
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.
Grants
Awarded by Australian Research Council
Funding Acknowledgements
We thank Peter Forrester and Ole Warnaar for discussions relating to the results presented here. D.R.'s research is supported by the Australian Research Council Discovery Project No. DP160101520 and the Australian Research Council Centre of Excellence for Mathematical and Statistical Frontiers No. CE140100049. S.W.'s research is supported by the Australian Research Council Discovery Early Career Researcher Award No. DE140101825 and the Australian Research Council Discovery Project No. DP160101520.