Perverse Sheaves on Real Loop Grassmannians
نویسنده
چکیده
The aim of this paper is to identify a certain tensor category of perverse sheaves on the real loop Grassmannian GrR of a real form GR of a connected reductive complex algebraic group G with the category of finite-dimensional representations of a reductive complex algebraic subgroup H of the dual group Ǧ. The root system of H is closely related to the restricted root system of GR. The fact that H is reductive implies that an interesting family of real algebraic maps satisfies the conclusion of the Decomposition Theorem of Beilinson-Bernstein-Deligne.
منابع مشابه
Perverse Sheaves on Grassmannians
We give a complete quiver description of the category of perverse sheaves on Hermitian symmetric spaces in types A and D, constructible with respect to the Schubert stratification. The calculation is microlocal, and uses the action of the Borel group to study the geometry of the conormal variety Λ.
متن کاملHow perverse is TQFT?
In this talk we will introduce Jones polynomial and Khovanov's homology of a knot. These topological invariants are (conjecturally) related to perverse sheaves on Grassmannians. We will try to understand how, and how understanding that might lead to new developments in Topological Quantum Field Theory.
متن کاملLectures by Joel Kamnitzer
One can define an action of sl2 on a category to be a sequence of categories with functors between them satisfying certain relations. Such actions were studied by Chuang-Rouquier in the context of representations of the symmetric group in positive characteristic. They used this action to build an equivalence of categories which settled a case of Broue’s conjecture. Later, Cautis, Licata, and th...
متن کاملPerverse sheaves on affine Grassmannians and Langlands duality
In this paper we outline a proof of a geometric version of the Satake isomorphism. Namely, given a connected, complex algebraic reductive group G we show that the tensor category of representations of the dual group G is naturally equivalent to a certain category of perverse sheaves on the affine Grassmannian of G. This can be extended to give a topological realization of algebraic representati...
متن کاملThe Affine Grassmannian
The affine Grassmannian is an important object that comes up when one studies moduli spaces of the form BunG(X), where X is an algebraic curve and G is an algebraic group. There is a sense in which it describes the local geometry of such moduli spaces. I’ll describe the affine Grassmannian as a moduli space, and construct it concretely for some concrete groups. References, including the constru...
متن کامل