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Gaudin subalgebras and stable rational curves
| Content Provider | Scilit |
|---|---|
| Author | Aguirre, Leonardo Felder, Giovanni Veselov, Alexander P. |
| Copyright Year | 2011 |
| Description | Journal: Compositio Mathematica 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 $\bar M_{0,n+1}$ . |
| Ending Page | 1478 |
| Starting Page | 1463 |
| ISSN | 00221295 |
| e-ISSN | 15705846 |
| DOI | 10.1112/s0010437x11005306 |
| Journal | Compositio Mathematica |
| Issue Number | 5 |
| Volume Number | 147 |
| Language | English |
| Publisher | Wiley-Blackwell |
| Publisher Date | 2011-09-01 |
| Access Restriction | Open |
| Subject Keyword | Journal: Compositio Mathematica Lie Algebra Moduli Space Algebraic Geometry 2 Dimensional First Order Differential Operators |
| Content Type | Text |
| Resource Type | Article |
| Subject | Algebra and Number Theory |
