2000 character limit reached
Verma modules for rank two Heisenberg-Virasoro algebra (1807.07735v1)
Published 20 Jul 2018 in math.RT
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.