Free field realization of the twisted Heisenberg–Virasoro algebra at level zero and its applications

Dražen Adamović ^[1] ; Gordan Radobolja ^[2]
1. [1] University of Zagreb
  
  University of Zagreb
  
  Croacia
2. [2] University of Split
  
  University of Split
  
  Croacia
Localización: Journal of pure and applied algebra, ISSN 0022-4049, Vol. 219, Nº 10 (October 2015), 2015, págs. 4322-4342
Idioma: inglés
DOI: 10.1016/j.jpaa.2015.02.019
Enlaces
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Resumen
- We investigate the free field realization of the twisted Heisenberg–Virasoro algebra H at level zero. We completely describe the structure of the associated Fock representations. Using vertex-algebraic methods and screening operators we construct singular vectors in certain Verma modules as Schur polynomials. We completely solve the irreducibility problem for the tensor products of irreducible highest weight modules with intermediate series. We also determine the fusion rules for an interesting subcategory of H-modules. Finally, as an application we present a free-field realization of the W(2,2)-algebra and interpret the W(2,2)-singular vectors as H-singular vectors in Verma modules.