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Title: Gaudin subalgebras and stable rational curves
Authors: Aguirre, Leonardo
Felder, G.
Veselov, A.P.
Keywords: Gaudin models
Kohno-Drinfeld Lie algebras
stable curves
Jucys-Murphy elements
Issue Date: 2011
Publisher: Cambridge University Press (© Foundation Compositio Mathematica)
Citation: AGUIRRE, L., FELDER, G. and VESELOV, A.P., 2011. Gaudin subalgebras and stable rational curves. Compositio Mathematica, 147 (5), pp. 1463-1478.
Abstract: Gaudin subalgebras are abelian Lie subalgebras of maximal dimension spanned by generators of the Kohno-Drinfeld Lie algebra tn. We show that Gaudin subalgebras form a variety isomorphic to the moduli space M 0;n+1 of stable curves of genus zero with n+1 marked points. In particular, this gives an embedding of M 0;n+1 in a Grassmannian of (n-1)-planes in an n(n-1)=2-dimensional space. We show that the sheaf of Gaudin subalgebras over M 0;n+1 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 M 0;n+1.
Description: The pubished version of this article is available at: http://dx.doi.org/10.1112/S0010437X11005306.
Version: Accepted for publication
DOI: 10.1112/S0010437X11005306
URI: https://dspace.lboro.ac.uk/2134/15216
Publisher Link: http://dx.doi.org/10.1112/S0010437X11005306
ISSN: 0010-437X
Appears in Collections:Published Articles (Maths)

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