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Whittaker modules for the principal W-algebra š¯’²k(sl3) via free field realizations

  • Dražen Adamović
  • Nina Yu
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Abstract

We study Whittaker and generalized Whittaker modules for the universal principal W-algebra š¯’²k(sl3), using two free field realizations: one in the Heisenberg vertex algebra of rank two and the other in the tensor product of the universal Virasoro vertex algebra with the Heisenberg vertex algebra of rank one. Under explicit conditions on the parameters, we construct universal Whittaker modules, establish their ordered bases, and obtain explicit irreducibility criteria. Under an explicit nondegeneracy condition, we also show that the submodules of these tensor products correspond to the submodules of the Virasoro factor. We prove irreducibility of the universal Whittaker modules constructed in this paper.

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Cite

BibTeXRIS
BibTeX
@misc{adamovic2026whittaker,
  title = {{Whittaker modules for the principal $W$-algebra $\mathcal W^k(\mathfraksl_3)$ via free field realizations}},
  author = {Dražen Adamović and Nina Yu},
  howpublished = {arXiv},
  year = {2026},
  month = nov,
  doi = {10.48550/arxiv.2611.01428},
  eprint = {2611.01428},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2611.01428},
}
RIS
TY  - UNPB
TI  - Whittaker modules for the principal W-algebra š¯’²^k(sl_3) via free field realizations
AU  - Dražen Adamović
AU  - Nina Yu
PY  - 2026
DA  - 2026/11/01
PB  - arXiv
DO  - 10.48550/arxiv.2611.01428
UR  - https://arxiv.org/abs/2611.01428
AB  - We study Whittaker and generalized Whittaker modules for the universal principal W-algebra š¯’²^k(sl_3), using two free field realizations: one in the Heisenberg vertex algebra of rank two and the other in the tensor product of the universal Virasoro vertex algebra with the Heisenberg vertex algebra of rank one. Under explicit conditions on the parameters, we construct universal Whittaker modules, establish their ordered bases, and obtain explicit irreducibility criteria. Under an explicit nondegeneracy condition, we also show that the submodules of these tensor products correspond to the submodules of the Virasoro factor. We prove irreducibility of the universal Whittaker modules constructed in this paper.
ER  -