Abstract
Inspired by automorphic forms and L-functions, B. Gross and D. Prasad published in 1992 conjectured about the restriction of irreducible tempered representations of special orthogonal groups SO(p + 1, q) to a special orthogonal subgroup SO(p, q).
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
J. Adams, D. Barbasch, D.A. Vogan, Jr., The Langlands Classification and Irreducible Characters for Real Reductive Groups. Progr. Math., vol. 104 (Birkhäuser Boston, Boston, MA, 1992)
J. Arthur, Classifying automorphic representations, in Current Developments in Mathematics 2012 (Int. Press, Somerville, MA, 2013), pp. 1–58
W.T. Gan, B.H. Gross, D. Prasad, J.-L. Waldspurger, Sur les conjectures de Gross et Prasad. I, in Astérique, vol. 346 (Soc. Math. France, 2012), xi+318 pp.
B.H. Gross, D. Prasad, On the decomposition of a representations of SOn when restricted to SOn−1. Can. J. Math. 44, 974–1002 (1992)
T. Kobayashi, B. Speh, Symmetry breaking for orthogonal groups and a conjecture by B. Gross and D. Prasad, in Geometric Aspects of the Trace Formula, Simons Symposia, ed. by W. Müller et al. (Springer, 2018), pp. 245–266. https://doi.org/10.1007/978-3-319-94833-1_8. Available also at arXiv:1702.00263. http://arxiv.org/abs/1702.00263
R.P. Langlands, On the Functional Equation Satisfied by Eisenstein Series. Lecture Notes in Math., vol. 544 (Springer, New York, 1976)
B. Sun, C.-B. Zhu, Multiplicity one theorems: the Archimedean case. Ann. Math. (2) 175, 23–44 (2012). http://dx.doi.org/10.4007/annals.2012.175.1.2
D.A. Vogan, Jr., The local Langlands conjecture, in Representation Theory of Groups and Algebras. Contemp. Math., vol. 145 (Amer. Math. Soc., Providence, RI, 1993), pp. 305–379
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2018 Springer Nature Singapore Pte Ltd.
About this chapter
Cite this chapter
Kobayashi, T., Speh, B. (2018). Application I: Some Conjectures by B. Gross and D. Prasad: Restrictions of Tempered Representations of SO(n + 1, 1) to SO(n, 1). In: Symmetry Breaking for Representations of Rank One Orthogonal Groups II. Lecture Notes in Mathematics, vol 2234. Springer, Singapore. https://doi.org/10.1007/978-981-13-2901-2_11
Download citation
DOI: https://doi.org/10.1007/978-981-13-2901-2_11
Published:
Publisher Name: Springer, Singapore
Print ISBN: 978-981-13-2900-5
Online ISBN: 978-981-13-2901-2
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)