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Part of the book series: Lecture Notes in Mathematics ((LNM,volume 2234))

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Abstract

A representation Π of a group G defines a representation of a subgroup G′ by restriction.

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References

  1. R. Beuzart-Plessis, A local trace formula for the Gan–Gross–Prasad conjecture for unitary groups: the archimedean case. ArXiv:1506.01452

    Google Scholar 

  2. D.H. Collingwood, Representations of Rank One Lie Groups. Res. Notes in Math., vol. 137 (Pitman (Advanced Publishing Program), Boston, MA, 1985), vii+244 pp.

    Google Scholar 

  3. 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.

    Google Scholar 

  4. 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)

    Article  Google Scholar 

  5. B.H. Gross, N. Wallach, Restriction of small discrete series representations to symmetric subgroups, in The Mathematical Legacy of Harish-Chandra, Baltimore, MD, 1998. Proc. Sympos. Pure Math., vol. 68 (Amer. Math. Soc., Providence, RI, 2000), pp. 255–272

    Google Scholar 

  6. A. Juhl, Families of Conformally Covariant Differential Operators, Q-Curvature and Holography. Progr. Math., vol. 275 (Birkhäuser Verlag, Basel, 2009)

    Google Scholar 

  7. A.W. Knapp, E.M. Stein, Intertwining operators for semisimple groups. Ann. Math. (2) 93, 489–578 (1971)

    Article  Google Scholar 

  8. T. Kobayashi, Discrete decomposability of the restriction of \(A_{\mathfrak {q}}(\lambda )\) with respect to reductive subgroups. III. Restriction of Harish-Chandra modules and associated varieties. Invent. Math. 131, 229–256 (1998). http://dx.doi.org/10.1007/s002220050203

  9. T. Kobayashi, A program for branching problems in the representation theory of real reductive groups, in Representations of Lie Groups. In Honor of David A. Vogan, Jr. on his 60th Birthday. Progr. Math., vol. 312 (Birkhäuser, 2015), pp. 277–322. http://dx.doi.org/10.1007/978-3-319-23443-4_10

  10. T. Kobayashi, T. Kubo, M. Pevzner, Conformal Symmetry Breaking Operators for Differential Forms on Spheres. Lecture Notes in Math., vol. 2170 (Springer, 2016), iv+192 pp. ISBN: 978-981-10-2657-7. http://dx.doi.org/10.1007/978-981-10-2657-7

  11. T. Kobayashi, T. Matsuki, Classification of finite-multiplicity symmetric pairs. Transform. Groups 19, 457–493 (2014). http://dx.doi.org/10.1007/s00031-014-9265-x. Special issue in honor of Dynkin for his 90th birthday

    Article  MathSciNet  Google Scholar 

  12. T. Kobayashi, B. Ørsted, P. Somberg, V. Souček, Branching laws for Verma modules and applications in parabolic geometry. I. Adv. Math. 285, 1796–1852 (2015). http://dx.doi.org/10.1016/j.aim.2015.08.020

    Article  MathSciNet  Google Scholar 

  13. T. Kobayashi, T. Oshima, Finite multiplicity theorems for induction and restriction. Adv. Math. 248, 921–944 (2013). http://dx.doi.org/10.1016/j.aim.2013.07.015

    Article  MathSciNet  Google Scholar 

  14. T. Kobayashi, B. Speh, Symmetry Breaking for Representations of Rank One Orthogonal Groups. Mem. Amer. Math. Soc., vol. 238 (Amer. Math. Soc., Providence, RI, 2015), v+112 pp. ISBN: 978-1-4704-1922-6. http://dx.doi.org/10.1090/memo/1126

    Article  MathSciNet  Google Scholar 

  15. B. Kostant, Verma modules and the existence of quasi-invariant differential operators, in Non-commutative Harmonic Analysis, Marseille–Luminy, 1974. Lecture Notes in Math., vol. 466 (Springer, Berlin, 1975), pp. 101–128

    Chapter  Google Scholar 

  16. M. Krämer, Multiplicity free subgroups of compact connected Lie groups. Arch. Math. (Basel) 27, 28–36 (1976)

    Article  MathSciNet  Google Scholar 

  17. C. Mœglin, J.-L. Waldspurger, Sur les conjectures de Gross et Prasad. II, in Astérique, vol. 347 (Soc. Math. France, 2012)

    Google Scholar 

  18. B. Sun, The nonvanishing hypothesis at infinity for Rankin–Selberg convolutions. J. Am. Math. Soc. 30, 1–25 (2017)

    Article  MathSciNet  Google Scholar 

  19. 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

    Article  MathSciNet  Google Scholar 

  20. N.R. Wallach, Real Reductive Groups. I. Pure Appl. Math., vol. 132 (Academic Press, Boston, MA, 1988), xx+412 pp. ISBN: 0-12-732960-9; II, ibid, vol. 132-II (Academic Press, Boston, MA, 1992), xiv+454 pp. ISBN: 978-0127329611

    Google Scholar 

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Acknowledgements

Many of the results were obtained while the authors were supported by the Research in Pairs program at the Mathematisches Forschungsinstitut MFO in Oberwolfach, Germany.

Research by the first author was partially supported by Grant-in-Aid for Scientific Research (A) (25247006) and (18H03669), Japan Society for the Promotion of Science.

Research by the second author was partially supported by NSF grant DMS-1500644. Part of this research was conducted during a visit of the second author at the Graduate School of Mathematics of The University of Tokyo, Komaba. She would like to thank it for its support and hospitality during her stay.

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Kobayashi, T., Speh, B. (2018). Introduction. 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_1

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