Compactly supported distributions on \(p\)-adic Lie groups (Q6610230)

In this article, the authors define the Iwasawa algebra \(K[[G]]\) for a \(p\)-adic field \(K\) and a \(p\)-adic Lie group \(G\), which is isomorphic to the convolution algebra of compactly supported distributions on \(G\) as topological algebras. Then the authors equip the continuous dual of an admissible \(K\)-Banach representation of \(G\) a structure of \(K[[G]]\)-algebra and extend Schneider-Teitelbaum duality to general \(p\)-adic groups. In particular, they use this formulation to prove the Frobenius reciprocity for continuous principal series on \(p\)-adic Banach spaces.