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

Symmetry Integrability and Geometry-Methods and Applications

article

Dražen Adamović¹  Gordan Radobolja² 

[1] Department of Mathematics, University of Zagreb;Faculty of Science, University of Split

关键词: Heisenberg–Virasoro Lie algebra;    vertex algebra;    W(2;    2) algebra;    screeningoperators;   

DOI  :  10.3842/SIGMA.2016.113

来源: National Academy of Science of Ukraine

【 摘 要 】

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.

【 授权许可】

Unknown