Skip to main content

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

Abstract

In this chapter we recall results about representations of the indefinite orthogonal group Gā€‰=ā€‰O(nā€‰+ā€‰1, 1).

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 49.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. A. Borel, N.R. Wallach, Continuous Cohomology, Discrete Subgroups, and Representations of Reductive Groups: Second edition. Math. Surveys Monogr., vol. 67 (Amer. Math. Soc., Providence, RI, 2000), xviii+260 pp.; First ed., Ann. of Math. Stud., vol. 94 (Princeton Univ. Press, Princeton, NJ, 1980), xvii+388 pp.

    Google ScholarĀ 

  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 ScholarĀ 

  3. T. Hirai, On irreducible representations of the Lorentz group of n-th order. Proc. Jpn. Acad. 38, 258ā€“262 (1962). https://projecteuclid.org/euclid.pja/1195523378

    ArticleĀ  MathSciNetĀ  Google ScholarĀ 

  4. A.W. Knapp, D.A. Vogan, Jr., Cohomological Induction and Unitary Representations. Princeton Math. Ser., vol. 45 (Princeton Univ. Press, Princeton, NJ, 1995), xx+948 pp. ISBN: 978-0-691-03756-6

    Google ScholarĀ 

  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

    ArticleĀ  MathSciNetĀ  Google ScholarĀ 

  7. H. Weyl, The Classical Groups. Their Invariants and Representations. Princeton Landmarks Math. (Princeton Univ. Press, Princeton, NJ, 1997)

    Google ScholarĀ 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

Copyright information

Ā© 2018 Springer Nature Singapore Pte Ltd.

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Kobayashi, T., Speh, B. (2018). Review of Principal Series Representations. 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_2

Download citation

Publish with us

Policies and ethics