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Hodge theory and unitary representations

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Representations of Reductive Groups

Part of the book series: Progress in Mathematics ((PM,volume 312))

Abstract

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

Dedicated to David Vogan, on the occasion of his sixtieth birthday

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References

  1. A. Beilinson and J. Bernstein, A proof of the Jantzen conjectures, Advances in Soviet Math. 16 (1993), 1–50.

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  4. W. Schmid and K. Vilonen, Hodge theory and unitary representations of reductive Lie groups, Frontiers of mathematical sciences, Int. Press, Somerville, MA, 2011, pp. 397–420.

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  5. D. A. Vogan, Jr., Signatures of hermitian forms and unitary representations, Slides of a talk at the Utah conference on Real Reductive Groups, 2009,http://www.math.utah.edu/realgroups/conference/conference-slides.html.

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Acknowledgements

The first author was supported in part by NSF grant DMS-1300185. The second author was supported in part by NSF grants DMS-1402928, DMS-1069316, and the Academy of Finland.

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Authors and Affiliations

  1. Department of Mathematics, Harvard University, Cambridge, MA, 02138, USA

    Wilfried Schmid

  2. Department of Mathematics, Northwestern University, Evanston, IL, 60208, USA

    Kari Vilonen

  3. Department of Mathematics, Helsinki University, Helsinki, Finland

    Kari Vilonen

Authors
  1. Wilfried Schmid
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  2. Kari Vilonen
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Corresponding author

Correspondence to Wilfried Schmid .

Editor information

Editors and Affiliations

  1. Department of Mathematics and Statistics, University of Ottawa, Ottawa, Ontario, Canada

    Monica Nevins

  2. Dept of Mathematics and Statistics, University of Utah, Salt Lake City, Utah, USA

    Peter E. Trapa

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Schmid, W., Vilonen, K. (2015). Hodge theory and unitary representations. In: Nevins, M., Trapa, P. (eds) Representations of Reductive Groups. Progress in Mathematics, vol 312. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-23443-4_16

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