Résume | Kazhdan and Laumon introduced a category constructed by glue-
ing W copies of the basic affine space. This category was studied by
Bezrukavnikov, Polishchuk and Morton-Ferguson. In particular some sub-
category was related to the representation theory of the small quantum
group uq .
In ongoing joint work with Morton-Ferguson we describe the Kazhdan-
Laumon category as a category of microlocal sheaves.
This localization is motivated by the relation between the small quan-
tum group and microlocal sheaves on the affine Springer fiber constructed
in ongoing joint work with Bezrukavnikov, McBreen and Yun. It should be
interpreted as understanding some subquotient category of uq − mod con-
structed by some stratification of the affine Springer fiber. Understanding
the filtration induced on the category by this stratification should have
applications to the representation theory of uq in particular to its center
and to the joint work with Bezrukavnikov, Shan and Vasserot.
In this talk I will discuss the connection between the Kazhdan-Laumon
category on the microlocal sheaves on affine Springer and this connection
to the small quantum group. |