We found a match
Your institution may have access to this item. Find your institution then sign in to continue.
- Title
Gaudin subalgebras and stable rational curves.
- Authors
Aguirre, Leonardo; Felder, Giovanni; Veselov, Alexander P.
- Abstract
Gaudin subalgebras are abelian Lie subalgebras of maximal dimension spanned by generators of the Kohno–Drinfeld Lie algebra $\Xmathfrak {t}_{\hspace *{.3pt}n}$. We show that Gaudin subalgebras form a variety isomorphic to the moduli space $\bar M_{0,n+1}$ of stable curves of genus zero with n+1 marked points. In particular, this gives an embedding of $\bar M_{0,n+1}$ in a Grassmannian of (n−1)-planes in an n(n−1)/2-dimensional space. We show that the sheaf of Gaudin subalgebras over $\bar M_{0,n+1}$ 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 $\bar M_{0,n+1}$.
- Subjects
LIE algebras; CURVES; RATIONAL points (Geometry); COMMUTATIVE algebra; DIFFERENTIAL operators; ISOMORPHISM (Mathematics); SHEAF theory
- Publication
Compositio Mathematica, 2011, Vol 147, Issue 5, p1463
- ISSN
0010-437X
- Publication type
Article
- DOI
10.1112/S0010437X11005306