Sine-Gordon Equation and Representations of Affine Kac–Moody Algebra sl2̂

✍ Scribed by Yuly Billig

• Publisher: Elsevier Science
• Year: 2002
• Tongue: English
• Weight: 220 KB
• Volume: 192
• Category: Article
• ISSN: 0022-1236
• DOI: 10.1006/jfan.2001.3915

✦ Synopsis

We give a representation-theoretic interpretation of the sine-Gordon equation using the action of affine Kac-Moody algebra sl 2 on the Weyl algebra. In this setup t-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.