monstrous moonshine
E656689
Monstrous moonshine is a deep and surprising connection between the Monster finite simple group and modular functions, revealing unexpected links between group theory, number theory, and string theory.
Observed surface forms (3)
| Surface form | Occurrences |
|---|---|
| Monster group | 0 |
| Monstrous Moonshine theory | 1 |
| theory of monstrous moonshine | 1 |
Statements (50)
| Predicate | Object |
|---|---|
| instanceOf |
finite simple group
ⓘ
mathematical theory ⓘ moonshine theory ⓘ |
| alsoKnownAs | Friendly Giant NERFINISHED ⓘ |
| associatedWith |
Monster vertex operator algebra V^natural
NERFINISHED
ⓘ
holomorphic CFT of central charge 24 ⓘ |
| awardRelated | Borcherds Fields Medal 1998 NERFINISHED ⓘ |
| centralStatement | McKay–Thompson series for Monster elements are Hauptmoduln for genus-zero groups ⓘ |
| conjectureDate | 1970s ⓘ |
| conjecturedBy |
John H. Conway
NERFINISHED
ⓘ
Simon P. Norton NERFINISHED ⓘ |
| connects |
Fourier coefficients of the j-function
ⓘ
Monster group NERFINISHED ⓘ j-invariant ⓘ modular forms of weight 0 ⓘ modular functions ⓘ representation theory of the Monster group ⓘ |
| field |
conformal field theory
ⓘ
group theory ⓘ modular forms ⓘ number theory ⓘ string theory ⓘ vertex operator algebras ⓘ |
| formulatedInPublication | Monstrous Moonshine (Conway–Norton, 1979) NERFINISHED ⓘ |
| hasKeyObject |
Hauptmodul
ⓘ
McKay–Thompson series NERFINISHED ⓘ Monster group NERFINISHED ⓘ modular j-function ⓘ moonshine module ⓘ vertex operator algebra V^natural ⓘ |
| hasKeyProperty |
Fourier coefficients encode dimensions of Monster representations
ⓘ
involves genus-zero modular functions ⓘ involves modular functions for subgroups of SL(2,ℝ) ⓘ relates q-expansions to character values ⓘ unexpected relation between finite simple groups and modular functions ⓘ uses graded representation of the Monster ⓘ |
| inspired |
Mathieu moonshine
ⓘ
generalized moonshine ⓘ umbral moonshine NERFINISHED ⓘ |
| order | 808017424794512875886459904961710757005754368000000000 ⓘ |
| proofDate | 1990s ⓘ |
| provedBy | Richard E. Borcherds NERFINISHED ⓘ |
| relatedTo |
Leech lattice
NERFINISHED
ⓘ
Niemeier lattices NERFINISHED ⓘ string theory on orbifolds ⓘ two-dimensional conformal field theory ⓘ |
| usesTool |
Borcherds–Kac–Moody algebras
NERFINISHED
ⓘ
automorphic forms ⓘ lattices ⓘ vertex operator algebras ⓘ |
Referenced by (4)
Full triples — surface form annotated when it differs from this entity's canonical label.
this entity surface form:
Monstrous Moonshine theory
this entity surface form:
theory of monstrous moonshine