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@SimonWadsley: Ah, I understand what you were getting at now! I am working on my phone, so I didn’t see the edit you made to your comment giving a more precise reference until after I replied.
@SimonWadsley: You calculate the character table (which can also be found in many other places), but on page 67 you say re the cuspidal representations “we won’t be able to explicitly construct the representations”.
This is really nice! Two questions: 1. Is there a friendly place to read about Kirillov models (I’m not a representation theorist)? and 2. I assume in your last sentence you mean the restriction of $\pi$ to $B$, right?