The $N=1$ super Heisenberg-Virasoro vertex algebra at level zero
Quantum Algebra
2020-11-25 v1 Mathematical Physics
math.MP
Representation Theory
Abstract
We study the representation theory of the N=1 super Heisenberg-Virasoro vertex algebra at level zero, which extends the previous work on the Heisenberg-Virasoro vertex algebra arXiv:math/0201314, arXiv:1405.1707 and arXiv:1703.00531 to the super case. We calculated all characters of irreducible highest weight representations by investigating certain Fock space representations. Quite surprisingly, we found that the maximal submodules of certain Verma modules are generated by subsingular vectors. The formulas for singular and subsingular vectors are obtained using screening operators appearing in a study of certain logarithmic vertex algebras in arXiv:0908.4053.
Keywords
Cite
@article{arxiv.2011.11989,
title = {The $N=1$ super Heisenberg-Virasoro vertex algebra at level zero},
author = {Drazen Adamovic and Berislav Jandric and Gordan Radobolja},
journal= {arXiv preprint arXiv:2011.11989},
year = {2020}
}
Comments
30 pages