Julia Yulia Gordon

In this dissertation, we combine the work of A. Aizenbud and D. Gourevitch on Schwartz functions on Nash manifolds, and the work of F. du Cloux on Schwartz inductions, to develop a toolbox of Schwartz analysis. We then use these tools to study the intertwining operators between parabolic inductions, and study the behavior of intertwining distributions on certain open subsets. Finally we use our results to give new proof of results in Bruhat's thesis on irreducibilities of degenerate principal series and minimal principal series.

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