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arXiv · 1903.04683

Odd singular vector formula for general linear Lie superalgebras

Jie Liu·Li Luo·Weiqiang Wang
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Abstract

We establish a closed formula for a singular vector of weight $\lambda-\beta$ in the Verma module of highest weight $\lambda$ for Lie superalgebra $\mathfrak{gl}(m|n)$ when $\lambda$ is atypical with respect to an odd positive root $\beta$. It is further shown that this vector is unique up to a scalar multiple, and it descends to a singular vector, again unique up to a scalar multiple, in the corresponding Kac module when both $\lambda$ and $\lambda-\beta$ are dominant integral.

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Jie Liu, Li Luo, Weiqiang Wang. 2019-03-12. Odd singular vector formula for general linear Lie superalgebras. https://arxiv.org/abs/1903.04683

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