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An analogue of the BGG resolution for locally analytic principal series. (English) Zbl 1219.22017
Let $$\mathbf G$$ be a connected reductive quasi-split algebraic group over a field $$L$$ which is a finite extension of the $$p$$-adic numbers. The author constructs an exact sequence modelled on (the dual of) the BGG resolution involving locally analytic principal series representations for $$\mathbf G(L)$$. This leads to an exact sequence involving spaces of overconvergent $$p$$-adic automorphic forms for certain groups which are compact modulo centre at infinity.

MSC:
 22E50 Representations of Lie and linear algebraic groups over local fields 11F55 Other groups and their modular and automorphic forms (several variables)
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References:
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