Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 12 (2016), 113, 13 pages      arXiv:1605.08608      https://doi.org/10.3842/SIGMA.2016.113

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

Dražen Adamović a and Gordan Radobolja b
a) Department of Mathematics, University of Zagreb, Bijenička 30, 10 000 Zagreb, Croatia
b) Faculty of Science, University of Split, Rudera Boškovića 33, 21 000 Split, Croatia

Received June 09, 2016, in final form December 03, 2016; Published online December 06, 2016; Several presentational changes made and misprints corrected January 15, 2017

Abstract
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.

Key words: Heisenberg-Virasoro Lie algebra; vertex algebra; $W(2,2)$ algebra; screening-operators.

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