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arXiv · 1807.07735

Verma modules for rank two Heisenberg-Virasoro algebra

Zhiqiang Li·Shaobin Tan
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Abstract

Let $\preceq$ be a compatible total order on the additive group $\mathbb{Z}^2$, and $L$ be the rank two Heisenberg-Virasoro algebra. For any $\mathbf{c}=(c_1,c_2,c_3,c_4) \in \mathbb{C}^4$, we define $\mathbb{Z}^2$-graded Verma module $M(\mathbf{c}, \preceq)$ for the Lie algebra $L$. A necessary and sufficient condition for the Verma module $M(\mathbf{c}, \preceq)$ to be irreducible is provided. Moreover, the maximal $\mathbb{Z}^2$-graded submodules of the Verma module $M(\mathbf{c}, \preceq)$ are characterized when $M(\mathbf{c}, \preceq)$ is reducible.

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Zhiqiang Li, Shaobin Tan. 2018-07-20. Verma modules for rank two Heisenberg-Virasoro algebra. https://arxiv.org/abs/1807.07735

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