2017/11/30 by David Ridout, Steve Siu, Simon Wood
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Algebra over a field #Algebraic structures and combinatorial models #Combinatorics #Mathematical physics #Mathematics #Nonlinear Waves and Solitons #Pure mathematics #math-ph #math.MP
paper · pdf · doi:10.1063/1.5019278
18 pages
openalex created_date 2017/12/22 · arxiv created 2018/02/25 · openalex publication_date 2018/03/01 · arxiv updated 2018/04/04 · openalex updated_date 2026/08/05
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.