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I posted my question here, but there is no reply yet. So, I guess I should post it on mathoverflow. I am reading the book of Schneider about Galois representation and $(\varphi, \Gamma)$-module, ...

I am reading Jackson - The theory of admissible representations of $\operatorname{GL}(2, F)$ and am not able to understand the following map related to Kirillov model. This result appears on p. 54: I ...