Cyclotomic level maps and associated varieties of simple affine vertex algebras
Fuente:
arXiv
Salvato in:
| Autori principali: | , , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2025
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866916844495962112 |
|---|---|
| author | Shan, Peng Yan, Wenbin Zhao, Qixian |
| author_facet | Shan, Peng Yan, Wenbin Zhao, Qixian |
| contents | In this paper, we introduce and study two cyclotomic level maps defined respectively on the set of nilpotent orbits $\underline{\mathcal{N}}$ in a complex semi-simple Lie algebra $\mathfrak{g}$ and the set of conjugacy classes $\underline{W}$ in its Weyl group, with values in positive integers. We show that these maps are compatible under Lusztig's map $\underline{W} \to \underline{\mathcal{N}}$, which is also the minimal reduction type map as shown by Yun. We also discuss their relationship with two-sided cells in affine Weyl groups.
We use these maps to formulate a conjecture on the associated varieties of simple affine vertex algebras attached to $\mathfrak{g}$ at non-admissible integer levels, and provide some evidence for this conjecture. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_09254 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Cyclotomic level maps and associated varieties of simple affine vertex algebras Shan, Peng Yan, Wenbin Zhao, Qixian Representation Theory Mathematical Physics Quantum Algebra In this paper, we introduce and study two cyclotomic level maps defined respectively on the set of nilpotent orbits $\underline{\mathcal{N}}$ in a complex semi-simple Lie algebra $\mathfrak{g}$ and the set of conjugacy classes $\underline{W}$ in its Weyl group, with values in positive integers. We show that these maps are compatible under Lusztig's map $\underline{W} \to \underline{\mathcal{N}}$, which is also the minimal reduction type map as shown by Yun. We also discuss their relationship with two-sided cells in affine Weyl groups. We use these maps to formulate a conjecture on the associated varieties of simple affine vertex algebras attached to $\mathfrak{g}$ at non-admissible integer levels, and provide some evidence for this conjecture. |
| title | Cyclotomic level maps and associated varieties of simple affine vertex algebras |
| topic | Representation Theory Mathematical Physics Quantum Algebra |
| url | https://arxiv.org/abs/2507.09254 |