# 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.

## 8 Citations

Hodge theory and unitary representations

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We describe our conjecture about the irreducible unitary representations of reductive Lie groups, in the special case of \(\mathrm{SL}(2, \mathbb{R})\).

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We prove the injectivity and vanishing theorem for R-Hodge modules and R-divisors over projective varieties, extending the results for rational Hodge modules and integral divisors in \cite{Wu15}. In…

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In this paper, we consider the star operations for (graded) affine Hecke algebras which preserve certain natural filtrations. We show that, up to inner conjugation, there are only two such star…

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