Gaudin subalgebras and stable rational curves

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 em...

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Main Authors:	Leonardo Aguirre, G. Felder, Alexander Veselov
Format:	Default Article
Published:	2011
Subjects:	Other mathematical sciences not elsewhere classified Gaudin models Kohno-Drinfeld Lie algebras stable curves Jucys-Murphy elements Mathematical Sciences not elsewhere classified
Online Access:	https://hdl.handle.net/2134/15216
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id	rr-article-9389165
record_format	Figshare
spelling	rr-article-93891652011-01-01T00:00:00Z Gaudin subalgebras and stable rational curves Leonardo Aguirre (7162031) G. Felder (7160177) Alexander Veselov (1259028) Other mathematical sciences not elsewhere classified Gaudin models Kohno-Drinfeld Lie algebras stable curves Jucys-Murphy elements Mathematical Sciences not elsewhere classified 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. 2011-01-01T00:00:00Z Text Journal contribution 2134/15216 https://figshare.com/articles/journal_contribution/Gaudin_subalgebras_and_stable_rational_curves/9389165 CC BY-NC-ND 4.0
institution	Loughborough University
collection	Figshare
topic	Other mathematical sciences not elsewhere classified Gaudin models Kohno-Drinfeld Lie algebras stable curves Jucys-Murphy elements Mathematical Sciences not elsewhere classified
spellingShingle	Other mathematical sciences not elsewhere classified Gaudin models Kohno-Drinfeld Lie algebras stable curves Jucys-Murphy elements Mathematical Sciences not elsewhere classified Leonardo Aguirre G. Felder Alexander Veselov Gaudin subalgebras and stable rational curves
description	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.
format	Default Article
author	Leonardo Aguirre G. Felder Alexander Veselov
author_facet	Leonardo Aguirre G. Felder Alexander Veselov
author_sort	Leonardo Aguirre (7162031)
title	Gaudin subalgebras and stable rational curves
title_short	Gaudin subalgebras and stable rational curves
title_full	Gaudin subalgebras and stable rational curves
title_fullStr	Gaudin subalgebras and stable rational curves
title_full_unstemmed	Gaudin subalgebras and stable rational curves
title_sort	gaudin subalgebras and stable rational curves
publishDate	2011
url	https://hdl.handle.net/2134/15216
_version_	1797467978215718912

Gaudin subalgebras and stable rational curves

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