Birational Weyl group action arising from a nilpotent Poisson algebra

Abstract

We propose a general method to realize an arbitrary Weyl group of Kac-Moody type as a group of birational canonical transformations, by means of a nilpotent Poisson algebra. We also give a Lie theoretic interpretation of this realization in terms of Kac-Moody Lie algebras and Kac-Moody groups.

31 pages, LaTeX

References in corpus (1)

• Universal exponential solution of the Yang-Baxter equation

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