High School Higher Dimensional Vectors

[Hornbein]

The 26 dimensional space of bosonic string theory could be denoted with alphabetical vectors.
[a,b,c,d,e,f,g,h,i,j,k,l,m,n,o,p,q,r,s,t,u,v,w,x,y,z,].

The 196,883 dimensions of the monster group could be represented with all possible sequences of the first 21 letters plus all possible sequences of the last seven letters, plus one more symbol, presumably "a".

So [a, aaaaaaaaaaaaaaaaaaaaa, aaaaaaaaaaaaaaaaaaaab, aaaaaaaaaaaaaaaaaaaac ... vvvvvvvvvvvvvvvvvvvvv, ttttttt, ttttttu, .... zzzzzzz ]

 

[jedishrfu]

Isn't it better to simply use subscripts for these types of vectors?

 

[martinbn]

A bit of a pedantic comment, but 196 883 is not the dimension of the group. It is the dimension of the minimal faithful representation (over the complex numbers).

 

[mathwonk]

Apparently it it's sort of like saying the alternating group A4, is 3 dimensional, since it equals the rotation group of the three dimensional tetrahedron. I.e. as martinbn says, it means the group occurs as the symmetry of an object (like a polytope) in n (possibly complex) dimensions.

https://mathoverflow.net/questions/355496/what-is-the-geometric-shape-of-the-monster-sporadic-group

 

[weirdoguy]

What's the point of this thread?

 

[Hornbein]

What's the point of anything?