Elliptic curves and birational representation of Weyl groups

2005/11/30 by Eguchi Mitsuaki, Mitsuaki, Eguchi, Tomoyuki Takenawa +1
Mathematics · #14H70 #Advanced Algebra and Geometry #Advanced Combinatorial Mathematics #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Primary 14E07 #Representation Theory (math.RT) #Secondary 14H52 #math.AG #math.RT #msc:14E07 #msc:14H52 #msc:14H70

paper · pdf · doi:10.48550/arxiv.math/0511726

14 pages

arxiv created 2005/11/30 · openalex publication_date 2005/11/30 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Some Weyl group acts on a family of rational varieties obtained by successive blow-ups at m (m≥ n+2) points in the projective space \mppⁿ(\mc). In this paper we study the case where all the points of blow-ups lie on a certain elliptic curve in \mppⁿ. Investigating the action of Weyl group on the Picard groups on the elliptic curve and on rational varieties, we show that the action on the parameters can be written as a group of linear transformations on the (m+1)-st power of a torus.

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• Integrability of n-dimensional dynamical systems of type E₇⁽¹⁾ and E₈⁽¹⁾

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