• Corpus ID: 118070696

Hodge theory and unitary representations of reductive Lie groups

@article{Schmid2011HodgeTA,
  title={Hodge theory and unitary representations of reductive Lie groups},
  author={Wilfried Schmid and Kari Vilonen},
  journal={arXiv: Representation Theory},
  year={2011},
  pages={397-420}
}
We present an application of Hodge theory towards the study of irreducible unitary representations of reductive Lie groups. We describe a conjecture about such representations and discuss some progress towards its proof. 
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References

SHOWING 1-10 OF 21 REFERENCES
The unitary spherical spectrum for split classical groups
  • D. Barbasch
  • Mathematics
    Journal of the Institute of Mathematics of Jussieu
  • 2010
Abstract This paper gives a complete description of the spherical unitary dual of split classical real and p-adic groups. The proof makes heavy use of the affine graded Hecke algebra.
Polarizable twistor D-modules
We prove a Decomposition Theorem for the direct image of an irreducible local system on a smooth complex projective variety under a morphism with values in another smooth complex projective variety.
Algebraic D-modules
Presented here are recent developments in the algebraic theory of D-modules. The book contains an exposition of the basic notions and operations of D-modules, of special features of coherent,
Differential Geometry and Symmetric Spaces
Elementary differential geometry Lie groups and Lie algebras Structure of semisimple Lie algebras Symmetric spaces Decomposition of symmetric spaces Symmetric spaces of the noncompact type Symmetric
Localization and standard modules for real semisimple Lie groups I: The duality theorem
In this paper we relate two constructions of representations of semisimple Lie groups constructions that appear quite different at first glance. Homogeneous vector bundles are one source of
Duality for vanishing cycle functors
Let Y be a complex manifold, and S an open disc. Put X=YxS9 and identify Y with Fx{0}. Let (M, F) be a holonomic filtered .S^-Module, i.e. M is holonomic and GrM is coherent over Gr3)x, where ^5Z is
On the Classification of Irreducible Representations of Real Algebraic Groups
Suppose G is a connected reductive group over a global field F . Many of the problems of the theory of automorphic forms involve some aspect of study of the representation ρ of G(A(F )) on the space
REPRESENTATION THEORY OF SEMISIMPLE GROUPS: An Overview Based on Examples
Page 55, proof of Lemma 3.13. This proof is incorrect as it stands because it involves an interchange of limits that has not been justified. A naive attempt to fix the proof might involve assuming
Variation of hodge structure: The singularities of the period mapping
Table of
Representations of reductive lie groups
ABSTRACT HARMONIC ANALYSIS PROBLEM 1.9. I. For a reasonable representation (TT, V) of a reasonable group G, show that (TT, V) is (in some reasonable sense) a "direct sum" of irreducible
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