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>"vertex" dual resonance theory Kac Moody algebra

Kac?Moody Lie algebra（下記）
”E. Date, M. Jimbo, M. Kashiwara, T. Miwa,(1983)
The vertex operator constructions were, quite unexpectedly, applied to the theory of soliton equations. This was based on the observation (see [DaJiKaMi])
The vertex operators were introduced in string theory around 1969, but the vertex operator construction entered string theory only at its revival in the mid 1980s. Thus, the representation theory of affine algebras became an important ingredient of string theory (see [GrScWi]).(1987)
The vertex operators turned out to be useful even in the theory of finite simple groups. Namely, a twist of the homogeneous vertex operator construction based on the Leech lattice produced the 196883-dimensional Griess algebra and its automorphism group, the famous finite simple Monster group (see Sporadic simple group) [FrLeMe].(1989)”
そうなんだ。Kac?Moody Lie algebraだったね

(参考)
https://encyclopediaofmath.org/wiki/Kac-Moody_algebra
15 November 2017
Kac-Moody algebra
A Kac-Moody algebra (also Kac?Moody Lie algebra) is defined as follows:
Let A=(aij)ni,j=1 be an (n×n)
-matrix satisfying conditions (see Cartan matrix)
aii=2;aij?0 aij=0 and aij∈Z for i≠j,⇒ aji=0.}(a1)
The associated Kac?Moody algebra g(A) is a Lie algebra over C on 3ngenerators ei, fi, hi
(called the Chevalley generators) and the following defining relations:
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