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Gaudin subalgebras and stable rational curves

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journal contribution
posted on 16.07.2014, 15:53 authored by Leonardo Aguirre, G. Felder, Alexander VeselovAlexander Veselov
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.

History

School

  • Science

Department

  • Mathematical Sciences

Published in

COMPOSITIO MATHEMATICA

Volume

147

Issue

5

Pages

1463 - 1478 (16)

Citation

AGUIRRE, L., FELDER, G. and VESELOV, A.P., 2011. Gaudin subalgebras and stable rational curves. Compositio Mathematica, 147 (5), pp. 1463-1478.

Publisher

Cambridge University Press (© Foundation Compositio Mathematica)

Version

AM (Accepted Manuscript)

Publication date

2011

Notes

The pubished version of this article is available at: http://dx.doi.org/10.1112/S0010437X11005306.

ISSN

0010-437X

eISSN

1570-5846

Language

en