Abstract
In 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 – pl η) = ∅ for all weights η > 0. Hence it is enough to understand the subquotients inside the dominant (or the antidominant) chamber.
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FIEBIG, P. PERIODICITY FOR SUBQUOTIENTS OF THE MODULAR CATEGORY 𝒪. Transformation Groups 28, 1081–1100 (2023). https://doi.org/10.1007/s00031-022-09770-4
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DOI: https://doi.org/10.1007/s00031-022-09770-4