The N=1 super Heisenberg-Virasoro vertex algebra at level zero

2020/11/24 by Drazen Adamovic, Adamovic, Drazen, Berislav Jandric +3 · 1 citation
Mathematics · Physics and Astronomy · #17B68 #17B69 #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Quantum Algebra (math.QA) #Representation Theory (math.RT) #math-ph #math.MP #math.QA #math.RT #msc:17B68 #msc:17B69

paper · pdf · doi:10.48550/arxiv.2011.11989

30 pages

arxiv created 2020/11/24 · arxiv updated 2020/11/25

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.

Citations

• Representations of the twisted Heisenberg-Virasoro algebra at level zero
• Self-dual and logarithmic representations of the twisted Heisenberg--Virasoro algebra at level zero
• On W-algebras associated to (2,p) minimal models and their representations

Cited by

• Representations of the N=1 Heisenberg-Virasoro superalgebra

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