The $N=1$ super Heisenberg-Virasoro vertex algebra at level zero
Drazen Adamovic, Berislav Jandric, Gordan Radobolja
TL;DR
This paper explores the representation theory of the N=1 super Heisenberg-Virasoro vertex algebra at level zero, revealing new structures like subsingular vectors and providing explicit character formulas for irreducible modules.
Contribution
It extends previous work on the Heisenberg-Virasoro algebra to the super case and computes all characters of irreducible highest weight representations.
Findings
Maximal submodules generated by subsingular vectors
Explicit formulas for singular and subsingular vectors
Characters of all irreducible highest weight modules
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.
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