Recent content by masnevets

Hi, To decompose a tensor product of representations of GL(n,C) into a direct sum of irreps, use the Littlewood-Richardson rule: http://en.wikipedia.org/wiki/Littlewood–Richardson_rule In your case, C^2 is the standard representation represented by the partition (1), and Sym^{N-2}(C^2) is...

okay I fixed them

Hi all, I am for some reason interested in creative or weird proofs of the fact that there are infinitely many prime numbers. I have started writing down all of the proofs that seemed sufficiently different in the following file: http://www.ocf.berkeley.edu/~ssam/primes.pdf If you know...

This is certainly not enough. You need to know that the representation is irreducible because for the trivial representation, we can just have all the entries mapping into a 2x2 identity matrix, and then the 01 entry of each matrix is 0. I don't know the answer yet, but I'll think about it...

I sent you a reply to the e-mail, so I look forward to meeting you tomorrow. But I'll say a few quick words about your post: EDIT: Actually, I had something here, but maybe I'd rather not say anything about people on the internet. Let's save it for in person. :)

Hi, I'm also a UC Berkeley math major. I'm finishing this semester and now I am in the fun/stressful stage of visiting grad schools and ultimately trying to decide where to go. I know of a guy from a few years ago who transferred in from a community college and then went on to Princeton...

Wikipedia is definitely not anywhere close to the amount of knowledge contained in math textbooks.

Most math departments don't like the general GRE, but it is a requirement for university admissions. From my understanding, most departments don't care much for the subject GRE score--if you do well, it won't help you, but if you do poorly, it raises a flag. I think it's particularly important...

I don't think it matters that you've completed a masters first.

Right, sorry I applied to seven schools. I really had no idea that any of those three schools would accept me. I was told by my advisor that I had a good shot, but that when it comes down to the final decisions, it's all a crapshoot. So I was basically told to apply to the "big 5" (Berkeley...

It's because American universities can be very fickle. There are no sure things. For example, I've been admitted to Princeton and MIT but got rejected from Harvard, whereas a friend of mine received the opposite treatment (accepted to Harvard but rejected from the other two).

that's a definition as far as I am concerned. How are you defining (f+g)(x)?

Well the left hand side \binom{\binom{n}{2}}{2} counts the number of unordered pairs of unordered pairs. What exactly can one look like? Either it involves 4 distinct elements, or it involves 3 distinct elements, like {{a,b}, {a,c}}, but it can never involve 2 or 1 distinct elements (why)? I...

I am exploiting linearity, yes. As mentioned above, to check that a map is injective in general, one needs to show that if f(x) = f(y), then x=y. But in the case of a linear map, f(x) = f(y) implies f(x-y) = 0, so you only need to check the case that something maps to zero. For onto, you can...

To show that a map is injective (one-to-one), you take some element x that maps to 0, and then prove that x has to be 0. So in your case, pick some x and y such that f(x,y) = 0. Then x-2y=0 and x+y =0. Since x=-y, the first equation becomes -3y=0, and so x=y=0.