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The Knapp–Stein Intertwining Operators Revisited: Renormalization and K-spectrum

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

Abstract

In this chapter, we discuss the classical Knapp–Stein operators, which may be viewed as a baby case of symmetry breaking operators (i.e., G = G′ case).

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References

  1. 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.

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

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  3. A.W. Knapp, E.M. Stein, Intertwining operators for semisimple groups. II. Invent. Math. 60, 9–84 (1980)

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  4. T. Kobayashi, Residue formula for regular symmetry breaking operators, in Contemp. Math., vol. 714 (Amer. Math. Soc., Province, RI, 2018), pp. 175–193 http://doi.org/10.1090/com/714/14380. Available also at arXiv:1709.05035. http://arxiv.org/abs/1709.05035

  5. 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

  6. 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 

  7. R.P. Langlands, On the Functional Equation Satisfied by Eisenstein Series. Lecture Notes in Math., vol. 544 (Springer, New York, 1976)

    Chapter  Google Scholar 

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Kobayashi, T., Speh, B. (2018). The Knapp–Stein Intertwining Operators Revisited: Renormalization and K-spectrum. 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_8

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