2017/03/31 by Drazen Adamovic, Gordan Radobolja · 1 citation
Mathematics · Physics and Astronomy · #math.QA #math-ph #math.MP #math.RT #msc:17B69 #msc:17B67 #msc:17B68 #msc:81R10
paper · pdf · doi:10.1142/s0219199718500086
published as Communications in Contemporary Mathematics, (2018) 1850008 (25 pages) · 22 pages, 6 figures
arxiv created 2018/03/30 · arxiv updated 2018/04/02
This paper is a continuation of arXiv:1405.1707. We present certain new applications and generalizations of the free field realization of the twisted Heisenberg-Virasoro algebra \mathcal H at level zero. We find explicit formulas for singular vectors in certain Verma modules. A free field realization of self-dual modules for \mathcal H is presented by combining a bosonic construction of Whittaker modules from arXiv:1409.5354 with a construction of logarithmic modules for vertex algebras. As an application, we prove that there exists a non-split self-extension of irreducible self-dual module which is a logarithmic module of rank two. We construct a large family of logarithmic modules containing different types of highest weight modules as subquotients. We believe that these logarithmic modules are related with projective covers of irreducible modules in a suitable category of \mathcal H-modules.