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I was trying to understand the paper "Forms of GL(2) from the analytic point of view", by Gelbart and Jacquet.

On Page 226 in Remark (4.13) they mention that the kernel of the local intertwining operator $M(\eta_{\nu})$ is has codimension one.

However, I cannot immediately see this. Any ideas?

I was trying to understand the paper "Forms of GL(2) from the analytic point of view", by Gelbart and Jacquet.

On Page 226 in Remark (4.13) they mention that the kernel of the local intertwining operator $M(\eta_{\nu})$ has codimension one.

However, I cannot immediately see this. Any ideas?

I was trying to understand the paper "Form of GL(2) from analaytic point of view", by Gelbart and Jacquet.

On Page 226 in Remark (4.13) they mention that the kernel of the local intertwining operator $M(\eta_{\nu})$ is has codimension one.

However, I cannot see immediately see this. Any ideas?

I was trying to understand the paper "Forms of GL(2) from the analytic point of view", by Gelbart and Jacquet.

On Page 226 in Remark (4.13) they mention that the kernel of the local intertwining operator $M(\eta_{\nu})$ is has codimension one.

However, I cannot immediately see this. Any ideas?