Transformation Groups

, Volume 10, Issue 3, pp 279-362

First online:

Modules over the small quantum group and semi-infinite flag manifold

  • S. ArkhipovAffiliated withDepartment of Mathematics, Yale University, New Haven, CT 06520 Email author 
  • , R. BezrukavnikovAffiliated withDepartment of Mathematics, Northwestern University, Evanston, IL 60208 Email author 
  • , A. BravermanAffiliated withDepartment of Mathematics, Brown University, Providence, RI 02912 and Einstein Institute of Mathematics, Edmond J. Safra Campus, Givat Ram, The Hebrew University of Jerusalem, Jerusalem, 91904 Email author 
  • , D. GaitsgoryAffiliated withDepartment of Mathematics, University of Chicago, Chicago, IL 60637 Email author 
  • , I. MirkovicAffiliated withDepartment of Mathematics, University of Massachusetts, Amherst, MA 01003 Email author 

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We develop a theory of perverse sheaves on the semi-infinite flag manifold G((t))/N((t)) · T[[t]], and show that the subcategory of Iwahori-monodromy perverse sheaves is equivalent to the regular block of the category of representations of the small quantum group at an even root of unity.