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Geometric Langlands duality and representations of algebraic groups over commutative rings
As such, it can be viewed as a first step in the geometric Langlands program. The connected complex reductive groups have a combinatorial classification by their root data. In the root datum the
Tilting exercises
We discuss tilting objects in categories of perverse sheaves smooth along some stratification. In case of the Schubert stratification we show that the Radon transform interchanges tilting,
Representations of semisimple Lie algebras in prime characteristic and the noncommutative Springer resolution
We prove most of Lusztig’s conjectures on the canonical basis in homology of a Springer ber. The conjectures predict that this basis controls numerics of representations of the Lie algebra of a
Equivariant homology and K-theory of affine Grassmannians and Toda lattices
For an almost simple complex algebraic group G with affine Grassmannian $\text{Gr}_G=G(\mathbb{C}(({\rm t})))/G(\mathbb{C}[[{\rm t}]])$, we consider the equivariant homology $H^{G(\mathbb{C}[[{\rm
Stability conditions for Slodowy slices and real variations of stability
We provide examples of an explicit submanifold in Bridgeland stabilities space of a local Calabi-Yau, and propose a new variant of definition of stabilities on a triangulated category, which we call
Singular Localization and Intertwining Functors for Reductive Lie Algebras in Prime Characteristic
In [BMR] we observed that, on the level of derived categories, representations of the Lie algebra of a semisimple algebraic group over a field of finite characteristic with a given (generalized)
Intersection cohomology of Drinfeld‚s compactifications
Abstract. Let X be a smooth complete curve, G be a reductive group and $ P \subset G $ a parabolic. Following Drinfeld, one defines a (relative) compactification $ \widetilde{\hbox{\rm Bun}\,}_P $
Characteristic cycles for the loop Grassmannian and nilpotent orbits
α (X), which is a linear combination of closures of conormal bundles to submanifolds of X. Intuitively, the microlocal multiplicities cα() me asurethesingularity of at α. In settings related to