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- W2950972166 abstract "Let $X$ be a (smooth and complete) curve and $G$ a reductive group. In [BG] we introduced the object that we called Eisenstein This is a perverse sheaf $bar{Eis}_E$ (or rather a complex of such) on the moduli stack $Bun_G(X)$ of principal $G$-bundles on $X$, which is attached to a local system $E$ on $X$ with respect to the torus $check{T}$, Langlands dual to the Cartan subgroup $Tsubset G$. In loc. cit. we showed that$bar{Eis}_E$ corresponds to the $check{G}$-local system induced from $E$, in the sense of the geometric Langlands correspondence. In the present paper we address the following question, suggested by V. Drinfeld: what is the perverse sheaf on $Bun_G(X)$ that corresponds to the universal deformation of $E$ as a local system with respect to the Borel subgroup $check{B}subset check{G}$? We prove, following a conjecture of Drinfeld, that the resulting perverse sheaf if the classical, i.e., non-compactified Eisenstein series." @default.
- W2950972166 created "2019-06-27" @default.
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- W2950972166 date "2006-05-04" @default.
- W2950972166 modified "2023-09-23" @default.
- W2950972166 title "Deformations of local systems and Eisenstein series" @default.
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