Titlebook: p-adic Banach Space Representations; With Applications to Dubravka Ban Book 2022 The Editor(s) (if applicable) and The Author(s), under exc

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Banach Space RepresentationsIn this chapter, we present the Schneider-Teitelbaum duality between Banach space representations and Iwasawa modules.

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Algebraic and Smooth RepresentationsIn this chapter, we review some basic properties of algebraic and smooth representations over an arbitrary field of characteristic zero.

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Continuous Principal SeriesIn this chapter, we define a continuous principal series representation and prove that it is an admissible Banach space representation. Its dual is an Iwasawa module. We describe this dual explicitly and then express it as a direct sum and also as a projective limit.

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Intertwining OperatorsIn this chapter, we prove that there are no intertwining operators between different principal series and that the only possible self-intertwining operators are scalar multiples of the identity map. In addition, we present some results on the irreducibility of continuous principal series representations.

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