Questions tagged [monster]
Questions about the Monster group, the largest of the sporadic simple groups. This group acts as symmetries on a vertex operator algebra whose graded dimension is the elliptic $j$-function.
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On level $10$ of the McKay-Thompson series of the Monster
(For brevity, the level-6 functions have been migrated to another post.)
I. Level-10 functions
Given the Dedekind eta function $\eta(\tau)$. To recall, for level-6,
$$j_{6A} = \left(\sqrt{j_{6B}} + \...
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Monstrous Langlands-McKay or what is bijection between conjugacy classes and irreducible representation for sporadic simple groups?
Context: The number of conjugacy classes equals to the number of irreducuble representations (over C) for any finite group. Moreover for the symmetric group and some other groups there is "good ...
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$H^4$ of the Monster
The Monster group $M$ acts on the moonshine vertex algebra $V^\natural$.
Because $V^\natural$ is a holomorphic vertex algebra (i.e., it has a unique irreducible module), there is a corresponding ...
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Why do these two Monster-related calculations yield $163$?
Fact 1: (1979, Conway and Norton)$^{1}$
"There are $194-22-9=\color{blue}{163\,}$ $\mathbb{Z}$-independent McKay-Thompson series for the Monster."
Note: There are 194 (linear) irreducible ...
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Why does the monster group exist?
Recently, I was watching an interview that John Conway did with Numberphile. By the end of the video, Brady Haran asked John:
If you were to come back a hundred years after your death, what problem ...
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What is the geometric shape of the Monster sporadic group?
Conway made the comment that the Monster group represents the symmetries of a shape in 196,883 dimensions, something like a "star you hang on a Christmas tree."
My question is, What do we know (or ...
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On level-$12$ of the McKay-Thompson series of the Monster and the Domb numbers
(This continues from level 10.) Given some moonshine functions $j_{N}$. There are nice descending and consistent relations for levels $6m$ with $m= 2,3,5,$
$$j_{12A} = \left(\sqrt{j_{12H}} + \frac{\...
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