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Gaudin subalgebras and stable rational curves

Published online by Cambridge University Press:  26 April 2011

Leonardo Aguirre
Affiliation:
Department of Mathematics, ETH Zurich, 8092 Zurich, Switzerland (email: [email protected])
Giovanni Felder
Affiliation:
Department of Mathematics, ETH Zurich, 8092 Zurich, Switzerland (email: [email protected])
Alexander P. Veselov
Affiliation:
Department of Mathematical Sciences, Loughborough University, Loughborough LE11 3TU, UK Moscow State University, Moscow 119899, Russia (email: [email protected])
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Abstract

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Gaudin subalgebras are abelian Lie subalgebras of maximal dimension spanned by generators of the Kohno–Drinfeld Lie algebra . We show that Gaudin subalgebras form a variety isomorphic to the moduli space of stable curves of genus zero with n+1 marked points. In particular, this gives an embedding of in a Grassmannian of (n−1)-planes in an n(n−1)/2-dimensional space. We show that the sheaf of Gaudin subalgebras over is isomorphic to a sheaf of twisted first-order differential operators. For each representation of the Kohno–Drinfeld Lie algebra with fixed central character, we obtain a sheaf of commutative algebras whose spectrum is a coisotropic subscheme of a twisted version of the logarithmic cotangent bundle of .

Type
Research Article
Copyright
Copyright © Foundation Compositio Mathematica 2011

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