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On Free Field Realizations of W(2, 2)-Modules

The aim of the paper is to study modules for the twisted Heisenberg–Virasoro algebra H at level zero as modules for the W(2, 2)-algebra by using construction from [J. Pure Appl. Algebra 219 (2015), 4322–4342, arXiv:1405.1707]. We prove that the irreducible highest weight H-module is irreducible as W(2, 2)-module if and only if it has a typical highest weight. Finally, we construct a screening operator acting on the Heisenberg–Virasoro vertex algebra whose kernel is exactly W(2, 2) vertex algebra.

Heisenberg–Virasoro Lie algebra ; vertex algebra ; W(2 ; 2) algebra ; screening- operators

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