Vincent
-
Member for 11 years, 2 months
-
Last seen this week
comment
Reference request: Oldest books on logic with unsolved exercises?
It is one of two common meanings, see Noah's comment on the original post. I was thinking about the other meaning
comment
Reference request: Oldest books on logic with unsolved exercises?
Which ones of these are unsolved?
comment
Continuous functions of three variables as superpositions of two variable functions
Yes, thank you! BTW I really like this answer.
comment
Continuous functions of three variables as superpositions of two variable functions
I agree with Pietor Majer about the two $g$s being confusing. Also it seems that user44191 proposed the notation $h$ for the second $g$ in the comments. Can you please use that notation in the answer as well?
comment
Why is the Fourier transform so ubiquitous?
Someone had to say it! +1
comment
Sign in Dirichlet's approximation theorem
What does the $\ll$ mean in this context?
comment
Computability of prime difference function
@NoahSchweber Can you clarify the issue in your last comment for me? I would expect that if the twin prime conjecture is undecidable then we have no way of computing the value of $f(2)$ for if we had, then we could just do the computation and hence decide the twin prime conjecture. Where do I go wrong?
Loading…
comment
Does the 3875-dimensional rep of $E_8$ have a solution to $x\star x=0$?
Ha, thank you. Now I think I see where my confusion is coming from. I was thinking of 'ordinary' $E_8$ rather than affine $E_8$. Thanks for your patience
comment
Does the 3875-dimensional rep of $E_8$ have a solution to $x\star x=0$?
@S.Carnahan Fair enough. I'll try to find some information online and maybe ask a separate question here or at MSE. Just one quick question, for $E8$ the basic representation and the adjoint representation are the same thing, aren't they?
comment
Does the 3875-dimensional rep of $E_8$ have a solution to $x\star x=0$?
@S.Carnahan thank you, but then I think my question is this: what representations do appear (through their dimension) in the Fourier series of the character? Why does 249 = 1 + 248 not appear?
comment
Does the 3875-dimensional rep of $E_8$ have a solution to $x\star x=0$?
I'm a bit confused by the equation $4124 = 1 + 248 + 3875$. Since we obviously also have $1 = 1$ shouldn't it follow by analogy that $248 = 1 + 248$? But that is clearly false. Can you explain what is going on here? Thanks in advance!
revised
Are primes linearly separable?
latexed some brackets
Loading…
comment
Regular graph such that $2$ distinct vertices have same neighborhood set
Why the downvote? I thought everybody loves Platonic solids?
revised
Open problems in Euclidean geometry?
Tried to clarify what the actual problem was (as I understand it from the linked article). Maybe my formulation can be improved.
Loading…
comment
Existence of four-dimensional real subspace
In the second to last line, should all the complement signs be there?
comment
How Does Random Noise Typically Look?
@KevinH.Lin I interpreted the picture as the straight line of green dots being the baseline for true random and the picture showing empirically that pi (red dots) is more random looking (that is: closer to the green line) than e (purple dots)
comment
Submodules of $V\otimes V^*$
Hmmm perhaps you are right, but be careful: having a semi-simple category is MUCH stronger than what I am claiming. There EVERY subrepresentation is a direct summand, I only claim that this very special submodule of these very special representations are. In other words: in the examples you give my argument works, BUT we do not even NEED my argument there since we can just say 'semi-simplicity' and be done with it, without looking into traces etc. So I still think there is something to check here.
comment
Submodules of $V\otimes V^*$
O where I wrote $n$ I meant $\dim V$. I was inadvertently thinking of my personal favorite module $V$ whose dimension just happens to be $n$
comment
Submodules of $V\otimes V^*$
Note that $W$ has an interpretation as the space of all linear maps (not just $U_q(\hat{\mathfrak{g}})$-maps but all of them) from $V$ to $V$. I believe the trivial module is sitting in there as the scalar multiples of the identity map. If this is true, then there is a natural projection operator $T: W \to \mathbb{C}I$ given by $x \mapsto \frac{1}{n} Trace(x)$. Clearly this is a linear projection operator (the second condition just says that $T \circ T = T$). So, as I said, what needs to be checked (or debunked) is that it is a $U_q(\hat{\mathfrak{g}})$-map. I leave that to you