2002-07-10
Sine-Gordon equation and representations of affine Kac-Moody algebra sl2
Publication
Publication
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.
| Additional Metadata | |
|---|---|
| Keywords | Kac-Moody algebras, Sine-Gordon equation, Weyl algebra |
| Persistent URL | dx.doi.org/10.1006/jfan.2001.3915 |
| Journal | Journal of Functional Analysis |
| Citation |
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
|