Local L-factors and perverse sheaves on certain loop spaces
Alexander Braverman (Brown University)
MSRI: Simons Auditorium
We present a conjectural construction of local L-factors for representations of a reductive group G over a local non-archimedian field of positive characteristic (associated with arbitrary algebraic representation of the Langlands dual group).The construction involves perverse sheaves on loop spaces into some algebraic semi-groups.
We prove that our construction gives the right answer for those representations of G which have an Iwahori-fixed vector. This is a joint work with R.Bezrukavnikov, M.Finkelberg and D.Kazhdan.