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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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