see also: https://www.youtube.com/watch?v=lbN8EMcOH5o On Thu, Apr 16, 2020 at 4:13 PM Brad Klee <bradklee@gmail.com> wrote:
Actually, I was thinking more in an analogy with groups for three-dimensional solids, where it is always possible, regardless of degree, to specify generators in terms of Euler angles + the so-called "Wigner D matrices". This should be more restrictive than asking for unitary or orthogonal matrices in general.
So I think this is probably not the case for Monster that group operations tie back into SO(3), this sounds wrong since the dimensions are so high.
Maybe there are super-rotations where the Euler angles and D matrices are generalized?
What I could be looking for, rather blindly and uncertainly, is a minimal set of parameters with some extra addition rules that give a cohesive explanation of //any// representation.
As far as I know, Conway was not satisfied with any of the proposed geometric interpretations. Unfortunately, I'm also ignorant as to what he would have considered a "good-enough" explanation. Any thoughts?
--Brad
On Thu, Apr 16, 2020 at 3:26 PM Victor Miller <victorsmiller@gmail.com> wrote:
If by rotations you mean orthogonal matrices, then, yes. It's a result (I think of Weyl) that, in the right basis, the image of the group elements by a representation is unitary. The wikipedia article on Monstrous Moonshine gives a good summary: https://en.wikipedia.org/wiki/Monstrous_moonshine
Victor
On Thu, Apr 16, 2020 at 3:44 PM Brad Klee <bradklee@gmail.com> wrote:
Here are a few more questions, possibly interesting, but currently beyond my depth:
Are all irreducible representations rotations?
If no, are any of the monster irreps rotational?
Does "Monstrous moonshine" imply that the J-invariant is a Hilbert Series for some rep. of monster group?
Or more specifically, can J(q) be computed by some sort of Molien equation or correlation table?
Do these last two questions make any sort of sense, or do they sound like drunken ravings?
In memoriam John Conway, right now could be a good time to throw out some speculation, even if it is over the moon, so to speak.
Cheers,
Brad _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
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