Affine Beilinson-Bernstein localization at the critical level for $GL_2$


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 $GL_2$ over a non-Archimedean field.


Sam Raskin

Department of Mathematics, The University of Texas at Austin, Austin, TX