Dec 12, 2009 20:04
OH MY GOD NARUTO SHIPPUUDEN Ep. 133 IS DONE SO WELL.
Yes, I know, months behind. Vacations are the time when I catch up on my Naturo episodes. But seriously, that one brought tears. Naruto makes me way too sentimental.
Also: Fall Quarter was a success this year. Let's see if I can do the same winter quarter, when I actually have hard classes
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Also, I haven't actually watched most of the Shippuuden episodes. I've seen the beginning and the end, but not much of the middle (I religiously read the manga on Fridays though). Sooooooooo gooood. But please don't fail out of school by watching Naruto, Yuri. Please don't =(.
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1) Prove the Peter-Weyl Theorem (This was not too hard, as we were given a mostly complete proof in the handouts, we just had to fill in the details)
2) Find two nontrivial irreducible representations who tensor to an irreducible representation (V_std \otimes V_sgn as a representation of S_4. Our TA (accidentally?) gave this one during his lectures on reps of S_n).
3) Give and prove the Weyl Integral Formula (haha. hahaha. Yeah, 'cause I know about Lie Groups and Manifolds, right?)
4) Compute the irreducible characters of O(n,R), SO(n,R), and Sp(2n) using the method of highest weights (Fairly long, but if I had started sooner, it wouldn't have been too bad.)
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