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).
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Notes
- 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
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A. Presley, G. Segal, in Loop Groups. Oxford Mathematical Monographs (Oxford Science Publications/The Clarendon Press, Oxford University Press/New York, 1986)
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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
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