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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

377 58- PDF

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

66 12- PDF

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

63 7- PDF

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

- R. Bezrukavnikov, M. Finkelberg, I. Mirkovic
- Mathematics
- Compositio 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

49 4

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

58 3

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

30 2

Semi-infinite flags. I. Case of global curve P 1 , Differential topology, infinite-dimensional Lie algebras, and applications

- I. Mirkovic
- 1999

1.1. We learnt of the Semiinfinite Flag Space from B.Feigin and E.Frenkel in the late 80-s. Since then we tried to understand this remarkable object. It appears that it was essentially constructed,… Expand

37 2

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