The Virasoro Algebra and the KP Hierarchy
A certain central extension of the Lie algebra of vector fields on the circle is called by physicists “the Virasoro algebra”. Mathematicians started to develop a representation theory of this algebra quite recently. The study of the highest weight representations of the Virasoro algebra was started by V. Kac ([4, 5]).
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- E. Date, M. Kashiwara, M. Jimbo and T. Miwa: Transformation groups for soliton equations, Proc. RIMS Symp. “Non-Linear Integrable Systems — Classical Theory and Quantum Theory”, M. Jimbo and T. Miwa ed., World Scientific Publishing Co., 1983, 39-119.Google Scholar
- V. G. Kac: Highest weight representations of infinite dimensional Lie algebras, in Proc. of ICM, 299-304, Helsinki, 1978.Google Scholar
- —: Infinite Dimensional Lie Algebras, Birkhäuser, 1983.Google Scholar
- N. R. Wallach: Classical invariant theory and the Virasoro algebra, preprint.Google Scholar
- H. Yamada: The basic representation of the extended affine Lie algebra of type A1(1) and the BKP hierarchy, to appear in Letters in Math. Phys.Google Scholar