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Let G be a connected split reductive group over a complete discrete valuationring of mixed characteristic. We use the theory of intermediate extensions dueto Abe-Caro and arithmetic Beilinson-Bernstein localization to classifyirreducible modules over the crystalline distribution algebra of G in terms ofoverconvergent isocrystals on locally closed subspaces in the (formal) flagvariety of G. We treat the case of SL(2) as an example.

Intermediate extensions and crystalline distribution algebras