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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

Characteristic cycles of constructible sheaves

- W. Schmid, K. Vilonen
- Mathematics
- 18 January 1996

In his paper [K], Kashiwara introduced the notion of characteristic cycle for complexes of constructible sheaves on manifolds: let X be a real analytic manifold, and F a complex of sheaves of… Expand

56 12- PDF

Whittaker patterns in the geometry of moduli spaces of bundles on curves

- E. Frenkel, D. Gaitsgory, K. Vilonen
- Mathematics
- 21 July 1999

Let G be a split connected reductive group over a finite field F_q, and N its maximal unipotent subgroup. V. Drinfeld has introduced a remarkable partial compactification of the moduli stack of… Expand

65 9- PDF

Perverse Sheaves on affine Grassmannians and Langlands Duality

- I. Mirkovi'c, K. Vilonen
- Mathematics
- 9 November 1999

This is an expanded version of the text ``Perverse Sheaves on Loop Grassmannians and Langlands Duality'', AG/9703010. The main new result is a topological realization of algebraic representations of… Expand

95 8- PDF

On the geometric Langlands conjecture

- E. Frenkel, D. Gaitsgory, K. Vilonen
- Mathematics
- 27 December 2000

Let X be a (smooth, projective) curve and G be a reductive group over a finite field Fq. The field KX of rational functions on X is what number theorists call a global field and we can do the theory… Expand

42 7- PDF

Characteristic cycles and wave front cycles of representations of reductive Lie groups

- W. Schmid, K. Vilonen
- Mathematics
- 1 May 2000

In the papers [V1] and [BV], Vogan and Barbasch-Vogan attach two similar invariants to representations of a reductive Lie group, one by an algebraic process, the other analytic. They conjectured that… Expand

60 3- PDF

On the geometry of nilpotent orbits

- W. Schmid, K. Vilonen
- Mathematics
- 2 October 2004

In this paper we obtain various results about the geometry of nilpotent orbits. In particular, we obtain a better understanding of the Kostant-Sekiguchi correspondence and Kronheimer's instanton… Expand

19 3- PDF

A geometric Jacquet functor

- M. Emerton, D. Nadler, K. Vilonen
- Mathematics
- 20 November 2003

In the paper [BB1], Beilinson and Bernstein used the method of localisation to give a new proof and generalisation of Casselman’s subrepresentation theorem. The key point is to interpret n-homology… Expand

17 2- PDF

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