Conversation started Jul 20, 2012 at 4:40.
anon
anon
Jul 20, 2012 04:40
k. In the same way that trees correspond to ways to fully parenthesize strings, we can use them to designate iterated commutators, like [[G,[G,G]],G]. Call it [G;T] for a given tree T. Then for what trees T and S is [G;T] a subgroup of [G;S] for all groups G? This vastly generalizes the lower central series embedding into the derived series.
For appropriately loose interpretation of "embedding."
Kannappan Sampath
Kannappan Sampath
@anon Hmm, I get the embedding part. And, it is very interesting.
I should review many things before attempting this.
anon
anon
On the same tack: we can use ordinal numbers to extend group series out beyond infinity via transfinite induction. I wonder if there's a good way to describe transfinite extension of these tree things.
Kannappan Sampath
Kannappan Sampath
Did you formulate the question yourself?
Peter Tamaroff
Peter Tamaroff
@HenryT.Horton Hey
anon
anon
I also had one inspired by percolation theory, about viewing inverse limits with random group theory by viewing the indexing set as something to percolate in that I mentioned to Eugene.
@KannappanSampath Yes.
Kannappan Sampath
Kannappan Sampath
Jul 20, 2012 04:45
@anon I know no percolation theory. :(
anon
anon
@KannappanSampath my knowledge of percolation theory is about equivalent to the AMS article I read on it
just the basic idea of percolation, wherein certain group extensions are activated with some probability, and then studying the limiting probability that the inverse limit has so-and-so properties.
Henry T. Horton
Henry T. Horton
@PeterTamaroff Hello, Peter, how are you doing, today,
Peter Tamaroff
Peter Tamaroff
@HenryT.Horton I was going to write something about that $1$-sphere thing.
Henry T. Horton
Henry T. Horton
Here in the states, we just call it a "circle"
Peter Tamaroff
Peter Tamaroff
Give me a sec
@HenryT.Horton I know that $f$ is continuous iff for every neighborhood $M$ of $f(a)$ there exists a neighborhood $N$ of $a$ such that $f(N) \subset M$.
I want to use that to prove the inverse is not continuous.
Kannappan Sampath
Kannappan Sampath
Jul 20, 2012 04:48
Also, I wanted to ask if you know some place where (most)all properties about character table or those properties of group that can be read off from there. @anon
anon
anon
I've only studied rep thry a little, but what's up?
I mean, obviously, conjugacy classes.
Kannappan Sampath
Kannappan Sampath
@anon Well, there are more trickier ones I know of (and is standard). I am sure there are many more hear-say things. :(
@MarianoSuárez-Alvarez May be you have some input here?
Henry T. Horton
Henry T. Horton
@PeterTamaroff Take a neighborhood of $0 \in [0, 2\pi)$ and a neighborhood of $(1,0) \in S^1$
anon
anon
you can derive character tables for tensor / symmetric / alternating powers of a rep from the rep's original char table
via theory of symmetric polynomials essentially
Kannappan Sampath
Kannappan Sampath
@anon I see. I am not aware of this. I'll read this up.
Henry T. Horton
Henry T. Horton
Jul 20, 2012 04:54
????
A neighborhood of $0 \in [0, 2\pi)$ is of the form $[0, \varepsilon)$
Peter Tamaroff
Peter Tamaroff
@HenryT.Horton Sorry, I was thinking about $0$ in $\Bbb R$. My bad.
anon
anon
@KannappanSampath here's a starting point
 
Conversation ended Jul 20, 2012 at 4:55.