geraldedgar comments on "While reading a book: Is this a typo or do I not understand?" (15353)

geraldedgar — Tue, 02 Aug 2011 07:33:58 -0700

... and if you first check whether there already exists an errata list for the book that mentions this ...

Qiaochu Yuan comments on "While reading a book: Is this a typo or do I not understand?" (15342)

Qiaochu Yuan — Mon, 01 Aug 2011 09:51:00 -0700

Sounds like a fine question to me as long as you try to make it reasonably self-contained.

Dror Speiser comments on "While reading a book: Is this a typo or do I not understand?" (15340)

Dror Speiser — Mon, 01 Aug 2011 08:39:26 -0700

Hello,

I'm reading this seminar book, and it claims something about something to the power of $q-1$. But, if I understood the text correctly, it should be $q+1$.
Is asking about such a specific thing legitimate?

* Since the specific situation might not look as specific as I'm afraid it does to others, I'll include the details (I guess you shouldn't read ahead if you already have an answer in mind):
"Seminar on algebraic groups and related finite groups", Borel, Carter, Curtis, Iwahori, Springer, Steinberg.
D. II. sec. 7.
The paragraph is talking about the induction from the Siegel parabolic of Sp4 of a cuspidal representation of the Levi. It says it is irreducible if and only if $\theta\ne\theta^q$. But, if I understand the relatively simple theory of GL2 (over a finite field!), if $\theta=\theta^q$ then the cuspidal representation itself isn't irreducible. If, on the other hand, $\theta^{-1}=\theta^q$, then the central character is trivial, and this makes the induction reducible (the longest root doesn't change the action).

Thanks,

Dror

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geraldedgar comments on "While reading a book: Is this a typo or do I not understand?" (15353)

Qiaochu Yuan comments on "While reading a book: Is this a typo or do I not understand?" (15342)

Dror Speiser comments on "While reading a book: Is this a typo or do I not understand?" (15340)