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
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
A. Beilinson and J. Bernstein, A proof of the Jantzen conjectures, Advances in Soviet Math. 16 (1993), 1–50.
H. Hecht, D. Miličić, W. Schmid and J. A. Wolf, Localization and standard modules for real semisimple Lie groups. I. The duality theorem, Invent. Math. 90 (1987), 297–332.
A. W. Knapp, Representation Theory of Semisimple Groups, An Overview Based on Examples, Princeton Landmarks in Mathematics, Princeton University Press, Princeton, NJ, 2001. Reprint of the 1986 original.
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.
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.
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.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2015 Springer International Publishing Switzerland
About this chapter
Cite this chapter
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
Download citation
DOI: https://doi.org/10.1007/978-3-319-23443-4_16
Published:
Publisher Name: Birkhäuser, Cham
Print ISBN: 978-3-319-23442-7
Online ISBN: 978-3-319-23443-4
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)