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Apr
28
awarded  Taxonomist
Mar
30
answered Signs in Chevalley's commutator formula
Mar
5
comment Is there a geometric construction of hyperbolic Kac-Moody groups?
But would one expect any sort of uniform geometric construction of these 238 groups? The only uniform constructions I know of Lie groups of type A-G are by Chevalley/Steinberg -- by generators and relations, like Tits for Kac-Moody groups. Otherwise, one finds these groups in a non-uniform manner by geometry -- e.g. type G_2 from octonions, etc.. So wouldn't one expect a large zoo of geometric constructions for the hyperbolic Kac-Moody groups?
Feb
5
comment The Weyl group of E8 versus $O_8^+(2)$
Yep - the kernel of $W \rightarrow O(\bar \Omega, N)$ is $\{ \pm 1 \}$.
Feb
4
revised The Weyl group of E8 versus $O_8^+(2)$
Hedged a bit due to confusions on notation.
Feb
4
comment The Weyl group of E8 versus $O_8^+(2)$
Incidentally, the notation issues with finite simple groups of Lie type in type $D$ are bemoaned at en.wikipedia.org/wiki/Group_of_Lie_type#Notation_issues.
Feb
4
revised The Weyl group of E8 versus $O_8^+(2)$
added 23 characters in body
Feb
4
answered The Weyl group of E8 versus $O_8^+(2)$
Jan
26
awarded  Yearling
Dec
21
awarded  Nice Question
Nov
23
awarded  Popular Question
Oct
19
comment Effective bound of $L(1,\chi)$
Thanks very much -- that's perfect!
Oct
18
asked Effective bound of $L(1,\chi)$
Oct
17
awarded  Nice Answer
Jul
26
comment Is the twisted symmetric fifth power $L$-function holomorphic?
@7-adic: Nope -- $Sym^5$ and higher are out of range of Langlands-Shahidi. Basically getting up to $Sym^4$ requires some special cases of Levi subgroups in exceptional groups, and sadly the special cases run out. Garland has a long-term program to try to extend these methods to infinite-dimensional groups -- if one is allowed to use Kac-Moody groups, one could go further. But alas, the results in that direction are not nearly strong enough for $Sym^5$ L-functions as far as I know.
Jul
7
comment Why is there a $\sqrt{5}$ in Hurwitz's Theorem?
My favorite proof is in Ford's aptly titled article "Fractions" (Amer. Math. Monthly, Vol 45, No 9 (Nov 1938)). He gives the "Ford circle" proof of Dirichlet's approximation theorem, and the $\sqrt{5}$ comes straight out of the geometry he uses. So, if "visual" suffices for "intuitive," this might suffice for your needs.
May
21
awarded  Nice Answer
Feb
24
comment $ n $-Cats-in-a-Bed Problem: Picking $ n $ points in a given planar domain to maximize the sum of their pairwise distances
In the case n=2, a Google image search indicates that pairs of cats in a bed tend not to maximize their pairwise distance. This may be a case of sampling bias however.
Feb
23
comment $ n $-Cats-in-a-Bed Problem: Picking $ n $ points in a given planar domain to maximize the sum of their pairwise distances
When $n=1$, the solution can be found at sleepingcatsw.com/images/cats/luther_bed.jpg
Jan
26
awarded  Yearling