Abstract
We prove the rank 1 case of a conjecture of Frenkel-Gaitsgory: critical level Kac-Moody representations with regular central characters localize onto the affine Grassmannian. The method uses an analogue in local geometric Langlands of the existence of Whittaker models for most representations of $\mathrm{GL}_2$ over a non-Archimedean field.
Citation
Sam Raskin. "Affine Beilinson-Bernstein localization at the critical level for $\mathrm{GL}_2$." Ann. of Math. (2) 195 (1) 251 - 335, January 2022. https://doi.org/10.4007/annals.2022.195.1.4
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