论文标题
$ n = 1 $ super Heisenberg-Virasoro顶点代数
The $N=1$ super Heisenberg-Virasoro vertex algebra at level zero
论文作者
论文摘要
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.我们通过研究某些FOCK空间表示来计算所有不可约的最高权重表示。令人惊讶的是，我们发现某些VERMA模块的最大s子模块是由内部向量产生的。使用筛选算子在ARXIV中的某些对数顶点代数的研究中出现的筛选算子获得了奇异载体的公式。0908.4053。
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.
