Quantization of nilpotent coadjoint $GL_N$-orbit closures in positive characteristics
Fuente:
arXiv
Salvato in:
| Autori principali: | , , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2026
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866917436301770752 |
|---|---|
| author | Ambrosio, Filippo Topley, Lewis Westaway, Matthew |
| author_facet | Ambrosio, Filippo Topley, Lewis Westaway, Matthew |
| contents | Let $G$ be a reductive group over an algebraically closed field of positive characteristic $p$, good for the root system of $G$. The closures of $G$-orbits in the Hilbert nullcone of the coadjoint representation are conical affine Poisson varieties, generically of full rank, known as {\em nilpotent coadjoint orbits}. In this paper, we classify the filtered Hamiltonian quantizations of these orbit closures for $G = GL_N$ and any $p > 0$. Our main new technique is a construction of quantizations from certain primitive quotients of the enveloping algebra, inducing them from the stabiliser in $G$ of the Frobenius twisted $p$-character. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_21597 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Quantization of nilpotent coadjoint $GL_N$-orbit closures in positive characteristics Ambrosio, Filippo Topley, Lewis Westaway, Matthew Representation Theory Rings and Algebras 17B45, 17B50, 17B63 Let $G$ be a reductive group over an algebraically closed field of positive characteristic $p$, good for the root system of $G$. The closures of $G$-orbits in the Hilbert nullcone of the coadjoint representation are conical affine Poisson varieties, generically of full rank, known as {\em nilpotent coadjoint orbits}. In this paper, we classify the filtered Hamiltonian quantizations of these orbit closures for $G = GL_N$ and any $p > 0$. Our main new technique is a construction of quantizations from certain primitive quotients of the enveloping algebra, inducing them from the stabiliser in $G$ of the Frobenius twisted $p$-character. |
| title | Quantization of nilpotent coadjoint $GL_N$-orbit closures in positive characteristics |
| topic | Representation Theory Rings and Algebras 17B45, 17B50, 17B63 |
| url | https://arxiv.org/abs/2604.21597 |