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Two-dimensional representations of affine Kac–Moody groups

✍ Scribed by Yu Chen

Publisher
Elsevier Science
Year
2002
Tongue
English
Weight
200 KB
Volume
252
Category
Article
ISSN
0021-8693

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✦ Synopsis

We give a complete and explicit description for all two-dimensional representations of non-twisted affine Kac-Moody groups. Those representations are found having a unique form characterized by homomorphisms between the base fields. The homomorphisms from affine Kac-Moody groups to two-dimensional linear groups are also determined.  2002 Elsevier Science (USA). All rights reserved.

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Sine-Gordon Equation and Representations
Sine-Gordon Equation and Representations of Affine Kac–Moody Algebra sl2̂
✍ Yuly Billig 📂 Article 📅 2002 🏛 Elsevier Science 🌐 English ⚖ 220 KB

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 p