The Kazhdan-Lusztig category of osp1|2n at irrational levels
Abstract
We prove the Kazhdan-Lusztig correspondence for the Lie superalgebra osp1|2n at irrational levels, that is, we show the category KLkev(osp1|2n) of finite-length even ordinary modules for the affine vertex operator superalgebra of osp1|2n at level k ∈ ℂ ∖ ℚ is braided tensor equivalent to the category of finite-dimensional even weight modules for the quantum group of osp1|2n at parameter q = eπi/(2k+2n+1). We also prove that KLkev(osp1|2n) is braided tensor equivalent to the category KLℓns(so2n+1) of finite-length ordinary modules with non-spinorial top level for the affine vertex operator algebra of so2n+1 at level ℓ such that $ \frac{1}{\ell+ 2n-1} = \frac{1}{2k+2n+1} + 1 \ \ ({\rm mod}\ 2\mathbb Z).$ Consequently, by gluing vertex operator (super)algebras via tensor categories, we construct a few new families of simple conformal vertex (super)algebras, including the mixed kernel VOAs that were the missing ingredient for proving certain Feigin-Frenkel type dualities in previous work of the first-named author with Linshaw, Nakatsuka, and Sato.
Related
- Hybrid Kazhdan-Lusztig basis and parabolic induction
- Real-rootedness of Kazhdan--Lusztig polynomials of sparse paving matroids
- Relative Rouquier linearity and inverse hybrid Kazhdan-Lusztig positivity
- Unimodality of Kazhdan--Lusztig polynomials of sparse paving matroids
- Prescribed Turán sign patterns for inverse Kazhdan-Lusztig polynomials of matroids
BibTeX
@misc{creutzig2026kazhdanlusztig,
title = {{The Kazhdan-Lusztig category of $\mathfrakosp_1|2n$ at irrational levels}},
author = {Thomas Creutzig and Robert McRae and Jinwei Yang},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.28094},
eprint = {2609.28094},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.28094},
}
RIS
TY - UNPB
TI - The Kazhdan-Lusztig category of osp_1|2n at irrational levels
AU - Thomas Creutzig
AU - Robert McRae
AU - Jinwei Yang
PY - 2026
DA - 2026/09/23
PB - arXiv
DO - 10.48550/arxiv.2609.28094
UR - https://arxiv.org/abs/2609.28094
AB - We prove the Kazhdan-Lusztig correspondence for the Lie superalgebra osp_1|2n at irrational levels, that is, we show the category KL_k^ev(osp_1|2n) of finite-length even ordinary modules for the affine vertex operator superalgebra of osp_1|2n at level k ∈ ℂ ∖ ℚ is braided tensor equivalent to the category of finite-dimensional even weight modules for the quantum group of osp_1|2n at parameter q = e^πi/(2k+2n+1). We also prove that KL_k^ev(osp_1|2n) is braided tensor equivalent to the category KL_ℓ^ns(so_2n+1) of finite-length ordinary modules with non-spinorial top level for the affine vertex operator algebra of so_2n+1 at level ℓ such that $ \frac{1}{\ell+ 2n-1} = \frac{1}{2k+2n+1} + 1 \ \ ({\rm mod}\ 2\mathbb Z).$ Consequently, by gluing vertex operator (super)algebras via tensor categories, we construct a few new families of simple conformal vertex (super)algebras, including the mixed kernel VOAs that were the missing ingredient for proving certain Feigin-Frenkel type dualities in previous work of the first-named author with Linshaw, Nakatsuka, and Sato.
ER -