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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 Schrödinger algebra and the N=1 3/2-conformal Galilei superalgebra, and over the complete spectrum-generating superalgebra in a special case.

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Cite

BibTeXRIS
BibTeX
@misc{gao2026quasiwhittaker,
  title = {{Quasi-Whittaker supermodules over Lie superalgebras}},
  author = {Wenting Gao and Baiying He and Shiyuan Liu and Jialin Xu},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.10968},
  eprint = {2609.10968},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.10968},
}
RIS
TY  - UNPB
TI  - Quasi-Whittaker supermodules over Lie superalgebras
AU  - Wenting Gao
AU  - Baiying He
AU  - Shiyuan Liu
AU  - Jialin Xu
PY  - 2026
DA  - 2026/09/10
PB  - arXiv
DO  - 10.48550/arxiv.2609.10968
UR  - https://arxiv.org/abs/2609.10968
AB  - 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 Schrödinger algebra and the N=1 3/2-conformal Galilei superalgebra, and over the complete spectrum-generating superalgebra in a special case.
ER  -