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arXiv · 2609.10968

Quasi-Whittaker supermodules over Lie superalgebras

Wenting Gao·Baiying He·Shiyuan Liu·Jialin Xu
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Abstract

In this paper, we develop a general theory of quasi-Whittaker supermodules over Lie superalgebras induced from an arbitrary ideal. We determine the quasi-Whittaker vectors in universal supermodules, establish an irreducibility criterion, and classify several families of irreducible supermodules. The odd part produces a new irreducibility phenomenon absent from the Lie algebra setting. As applications, we determine all irreducible quasi-Whittaker supermodules over the $N=1$ super Schr\"odinger algebra and the $N=1$ $\frac{3}{2}$-conformal Galilei superalgebra, and over the complete spectrum-generating superalgebra in a special case.

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BibTeXRIS

Wenting Gao, Baiying He, Shiyuan Liu, Jialin Xu. 2026-09-10. Quasi-Whittaker supermodules over Lie superalgebras. https://arxiv.org/abs/2609.10968

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