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On Free Field Realizations of $W(2,2)$-Modules
Symmetry, integrability and geometry: methods and applications, Tome 12 (2016) Cet article a éte moissonné depuis la source Math-Net.Ru

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The aim of the paper is to study modules for the twisted Heisenberg–Virasoro algebra $\mathcal H$ 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 ${\mathcal H}$-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.
Keywords: Heisenberg–Virasoro Lie algebra; vertex algebra; $W(2,2)$ algebra; screening-operators. 
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     author = {Dra\v{z}en Adamovi\'c and Gordan Radobolja},
     title = {On {Free} {Field} {Realizations} of $W(2,2)${-Modules}},
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     year = {2016},
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     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SIGMA_2016_12_a112/}
}
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Dražen Adamović; Gordan Radobolja. On Free Field Realizations of $W(2,2)$-Modules. Symmetry, integrability and geometry: methods and applications, Tome 12 (2016). http://geodesic.mathdoc.fr/item/SIGMA_2016_12_a112/

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