PreprintCC BY 4.0arXiv
On minimal singular vectors of Vκ(g) for types B and C
Abstract
Let g be a finite-dimensional simple Lie algebra of type B or C over ℂ. Given κ∈ℂ, let Vκ(g) be the universal affine vertex algebra associated with g at level κ. We characterize the weights of minimal singular vectors of Vκ(g) with respect to the generalized Cartan matrix, when Vκ(g) is not simple and κ is not critical. Furthermore, we determine the corresponding longest Weyl elements in the Kashiwara-Tanisaki character theorem of the singular vectors.
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BibTeX
@misc{jiang2026minimal,
title = {{On minimal singular vectors of $V^κ(\mathfrakg)$ for types $B$ and $C$}},
author = {Cuipo Jiang and Tong Wu},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.07917},
eprint = {2611.07917},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.07917},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - On minimal singular vectors of V^κ(g) for types B and C
AU - Cuipo Jiang
AU - Tong Wu
PY - 2026
DA - 2026/11/05
PB - arXiv
DO - 10.48550/arxiv.2611.07917
UR - https://arxiv.org/abs/2611.07917
AB - Let g be a finite-dimensional simple Lie algebra of type B or C over ℂ. Given κ∈ℂ, let V^κ(g) be the universal affine vertex algebra associated with g at level κ. We characterize the weights of minimal singular vectors of V^κ(g) with respect to the generalized Cartan matrix, when V^κ(g) is not simple and κ is not critical. Furthermore, we determine the corresponding longest Weyl elements in the Kashiwara-Tanisaki character theorem of the singular vectors.
ER -