Sine-Gordon equation and representations of affine Kac-Moody algebra sl2
Journal of Functional Analysis , Volume 192 - Issue 2 p. 295- 318
We give a representation-theoretic interpretation of the sine-Gordon equation using the action of affine Kac-Moody algebra sl2 on the Weyl algebra. In this setup τ-functions become functions in non-commuting variables. The skew Casimir operators that we introduce here, give rise to a hierarchy of partial differential equations that includes the sine-Gordon equation and two copies of the Korteweg-de Vries equation.
|Kac-Moody algebras, Sine-Gordon equation, Weyl algebra|
|Journal of Functional Analysis|
|Organisation||School of Mathematics and Statistics|
Billig, Y. (2002). Sine-Gordon equation and representations of affine Kac-Moody algebra sl2. Journal of Functional Analysis, 192(2), 295–318. doi:10.1006/jfan.2001.3915