Gaitsgory, DennisRaskin, Samuel2014-06-062014-06-062014Raskin, Samuel David. 2014. Chiral Principal Series Categories. Doctoral dissertation, Harvard University.http://dissertations.umi.com/gsas.harvard:11525http://nrs.harvard.edu/urn-3:HUL.InstRepos:12274305This thesis begins a study of principal series categories in geometric representation theory using the Beilinson-Drinfeld theory of chiral algebras. We study Whittaker objects in the unramified principal series category. This provides an alternative approach to the Arkhipov-Bezrukavnikov theory of Iwahori-Whittaker sheaves that exploits the geometry of the Feigin-Frenkel semi-infinite flag manifold.en-USMathematicsAlgebraAlgebraic geometryAutomorphic formsGeometric LanglandsRepresentation theoryThesis or Dissertation2014-06-06