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Birational Weyl group action arising from a nilpotent Poisson algebra

Masatoshi Noumi·Yasuhiko Yamada
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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.

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Masatoshi Noumi, Yasuhiko Yamada. 2000-12-05. Birational Weyl group action arising from a nilpotent Poisson algebra. https://doi.org/10.1142/9789812810199_0010

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