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Characteristic varieties of character sheaves
Ivan Mirković,Kari Vilonen +1 more
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This article is published in Inventiones Mathematicae.The article was published on 1988-06-01. It has received 79 citations till now. The article focuses on the topics: Direct image with compact support & Base change.read more
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Geometric Langlands duality and representations of algebraic groups over commutative rings
Ivan Mirković,Kari Vilonen +1 more
TL;DR: In this article, the basic relationship between G and G is discussed, and a canonical construction of G, starting from G, is presented, which leads to a rather explicit construction of a Hopf algebra by Tannakian formalism.
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Character sheaves on disconnected groups, X
TL;DR: In this paper, the unipotent character sheaves on a fixed connected component of a reductive algebraic group were classified under a mild hypothesis on the characteristic of the ground field.
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The Character Theory of a Complex Group
David Ben-Zvi,David Nadler +1 more
TL;DR: In this paper, the authors apply the ideas of derived algebraic geometry and topological field theory to the representation theory of reductive groups and establish parallel properties of the Hecke category, showing it is a two-dualizable Calabi-Yau monoidal category.
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Finite-dimensional representations of DAHA and affine Springer fibers: The spherical case
Michela Varagnolo,E. Vasserot +1 more
TL;DR: In this paper, the authors classify finite-dimensional simple spherical representations of rational double affine Hecke algebras, and study a remarkable family of finite dimensional simple spherical representation of double-affine hecke Algebraes.
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Geometric Langlands duality and representations of algebraic groups over commutative rings
Ivan Mirković,Kari Vilonen +1 more
TL;DR: In this paper, a geometric version of the Satake isomorphism is given for a connected complex reductive algebraic group, where the category of representations of its Langlands dual is naturally equivalent to a certain category of perverse sheaves on the complex affine Grassmannian.
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Character sheaves, V
TL;DR: The character sheaves on a connected reductive algebraic group G have been studied in this article, where it is shown that under certain assumptions, there is a natural surjective map with finite fibers from G to the set of all pairs (9, c) up to conjugacy by the Weyl group.
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Characteristic varieties and vanishing cycles.
TL;DR: The authors present an etude systematique des varietes caracteristiques des systemes holonomes a singularites regulieres coniques dans le fibre cotangent T * X