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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5
votes
0answers
143 views

Monster group as automorphism group of a distributive lattice

It is known that every finite group is the automorphism group of a finite distributive lattice. Question: What is the minimal order of a distributive lattice $L$ such that the automorphism group of $...
8
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1answer
357 views

Is $J_1$ a subquotient of the monster group?

Edit: I was able to make a 3D diagram of the happy family if anyone is interested! https://www.youtube.com/watch?v=_4IjnIcECoQ I'm working on a twitter thread about the monster group, because I saw ...
19
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3answers
2k views

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 ...
1
vote
1answer
169 views

Where can I find a table of the exponents of the sporadic groups?

Is there a table showing Sporadic Groups and their exponents, and, perhaps, other basic properties. In particular, I'm interested in what the exponent of the Monster Group is. (Obviously the order is ...
17
votes
1answer
806 views

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 ...
22
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1answer
751 views

71, the Monster, and c = 24 CFTs

The largest prime in the order of the Monster group is $71$. This number $71$ shows up at various places: The minimal faithful representation has dimension $196883 = 47.59.71$ The Monster group can ...
16
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0answers
598 views

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 ...
4
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0answers
294 views

The largest primes in the monster group construction

The last three prime numbers in the factorization of the order of the Fischer Griess friendly monster group are 47, 59, 71. (https://en.wikipedia.org/wiki/Monster_group) On the other hand, the monster ...
6
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0answers
313 views

Sporadic and Exceptional

I have been reading this recent paper of J.McKay and YH. He (they've written a number of papers recently, including a fun and joking one on 42 which overflow commented on) called "Sporadic and ...
10
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1answer
991 views

A curious property of Ramanujan's function $\tau(n)$

As it is well known, Ramanujan's $\tau(n)$ function can be defined through the power series expansion of the modular discriminant: $$\Delta(q)=q\prod\limits_{n=1}^\infty (1-q^n)^{24}=\sum \limits_{n=...
3
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0answers
114 views

“A locally dual polar space for the Monster”

I am currently looking at Ronan and Stroth's 1984 paper Minimal Parabolic Geometries for the Sporadic Groups. When considering the $3$-minimal parabolic system of $F_{1}$, they cite a preprint by ...
5
votes
2answers
379 views

Computing Thompson Series for the Monster Group

I am trying to do some experimentation with the values of Thompson series, but I have having a hard time finding a table that has these Thompson series with as many terms as I'd like. The tables I've ...
43
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2answers
3k views

$H^4$ 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 ...
19
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1answer
4k views

The Monster Group uses in mathematical physics

I am doing a project on the inverse Galois problem, and am seeking to show that the monster group is realisable over the rationals. I have heard that the monster group has found uses in theoretical ...
5
votes
2answers
348 views

FLM-like construction of VOA for other simple groups

Frenkel, Lepowsky, Meurman constructed the vertex operator algebra (VOA) $V^\natural$ as a chiral orbifold CFT whose target space is $\mathbb{R}^{24}/\Lambda/\mathbb{Z}_2$. (Here the last $\mathbb{Z}...