Abstract
This section corresponds to the discussion in §1.4 of the Introduction. For \(\Gamma \) an admissible, simple component of C r(L, d), we consider the relative Infinite Grassmannian over \(\breve{\Gamma }\) associated to the sheaf of Lie algebras \(\boldsymbol{{\mathcal{G}}}^{{\prime}}_{\mbox{ $\Gamma $}}\) (see (11.5) for notation).
Keywords
- Fibre Bundle
- Weyl Group
- Cartan Subalgebra
- Tensor Category
- Perverse Sheave
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
This is a preview of subscription content, access via your institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsNotes
- 1.
These are the Lie algebras \(\mathbf{sl}({H}^{0}(\mathcal{O}_{{Z}^{{\prime}}}))\), for \([Z] \in \breve{ \Gamma }\).
- 2.
Recall from (11.1): \(\boldsymbol{\mathcal{G}}_{\mbox{ $\Gamma $}} = \mbox{ ${\pi }^{{\ast}}\mathbf{sl}({\mathcal{F}}^{{\prime}})$}\).
- 3.
See §6 for details about sl 2-triples associated to d + (v).
- 4.
References
V. Ginzburg, Perverse sheaves on a loop group and Langlands duality [arxiv: alg-geom/ 9511007]
G. Lusztig, in Singularities, Character Formulas, and a q-Analog of Weight Multiplicities. Analysis and Topology on Singular Spaces, II, III. Astérisque. Soc. Math. France, Paris vol. 101–102 (Luminy, 1981), pp. 208–229
I. Mirkovič, K. Vilonen, Geometric Langlands duality and representations of algebraic groups over commutative rings. Ann. Math. (2) 166(1), 95–143 (2007)
A. Presley, G. Segal, in Loop Groups. Oxford Mathematical Monographs (Oxford Science Publications/The Clarendon Press, Oxford University Press/New York, 1986)
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2013 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Reider, I. (2013). J(X; L, d) and the Langlands Duality. In: Nonabelian Jacobian of Projective Surfaces. Lecture Notes in Mathematics, vol 2072. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-35662-9_12
Download citation
DOI: https://doi.org/10.1007/978-3-642-35662-9_12
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-35661-2
Online ISBN: 978-3-642-35662-9
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)
