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Geometric Langlands duality and representations of algebraic groups over commutative rings

- I. Mirkovic, K. Vilonen
- Mathematics
- 18 January 2004

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… Expand

Tilting exercises

- A. Beilinson, R. Bezrukavnikov, I. Mirkovic
- Mathematics
- 10 January 2003

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,… Expand

Representations of semisimple Lie algebras in prime characteristic and the noncommutative Springer resolution

- R. Bezrukavnikov, I. Mirkovic, with an Appendix by Eric Sommers
- Mathematics
- 14 January 2010

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… Expand

Equivariant homology and K-theory of affine Grassmannians and Toda lattices

- R. Bezrukavnikov, M. Finkelberg, I. Mirkovic
- MathematicsCompositio Mathematica
- 21 April 2005

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… Expand

Stability conditions for Slodowy slices and real variations of stability

- R. Anno, R. Bezrukavnikov, I. Mirkovic
- Mathematics
- 7 August 2011

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… Expand

Singular Localization and Intertwining Functors for Reductive Lie Algebras in Prime Characteristic

- R. Bezrukavnikov, I. Mirkovic, D. Rumynin
- MathematicsNagoya Mathematical Journal
- 4 February 2006

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)… Expand

Intersection cohomology of Drinfeld‚s compactifications

- A. Braverman, M. Finkelberg, D. Gaitsgory, I. Mirkovic
- Mathematics
- 15 December 2000

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 $… Expand

Characteristic cycles for the loop Grassmannian and nilpotent orbits

- S. Evens, I. Mirkovic
- Mathematics
- 1 March 1999

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… Expand

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