Abstract
AbstractIn this paper we study the category 𝒪 over the hyperalgebra of a reductive algebraic group in positive characteristics. For any locally closed subset K of weights, we define a subquotient 𝒪[K] of 𝒪. It has the property that its simple objects are parametrized by elements in K. We then show that 𝒪[K] is equivalent to 𝒪 [K +pl γ] for any dominant weight γ if l > 0 is an integer such that K ∩ (K – plη) = ∅ for all weights η > 0. Hence it is enough to understand the subquotients inside the dominant (or the antidominant) chamber.
Publisher
Springer Science and Business Media LLC
Subject
Geometry and Topology,Algebra and Number Theory
Reference11 articles.
1. H. H. Andersen, BGG categories in prime characteristics, arxiv:2106.00057 (2021).
2. И. Н. Бернштейн, И. М. Гельфанд, С. И. Гельфанд, Об одной категории 𝔤-модуль, Φункц. анализ и его прил. 10 (1976), вып. 2, 1–8. Engl. transl.: J. Bernshtein, I. M. Gel’fand, S. I. Gel’fand, Category of 𝔤-modules, Functional. Anal. and its Appl. 10 (1976), no. 2, 87–92.
3. C. Chevalley, Certains schémas de groupes semi-simples, Séminaire Bourbaki (1960–1961), 2e éd., Vol. 6, Paris, 1961, pp. 219–234.
4. Deodhar, V.V., Gabber, O., Kac, V.G.: Structure of some categories of representations of infinite-dimensional Lie algebras. Adv. in Math. 45, 92–116 (1982)
5. Fiebig, P.: The combinatorics of category 𝒪 over symmetrizable Kac–Moody algebras. Transform. Groups. 11, 29–49 (2006)
Cited by
1 articles.
订阅此论文施引文献
订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献
1. Quantum tilting modules over local rings;Journal of the London Mathematical Society;2023-01-11