Skip to main content
SpringerLink
Log in
Book cover

Representations of Reductive p-adic Groups pp 161–174Cite as

Birkhäuser

Classification of Strongly Positive Representations of Even General Unitary Groups

  • Chapter
  • First Online:

  • 687 Accesses

Part of the book series: Progress in Mathematics ((PM,volume 328))

Abstract

We explicitly identify the structure of Jacquet modules of parabolically induced representations of even unitary groups and even general unitary groups over a p-adic field F of characteristic different than two. As an application, we obtain a classification of the strongly positive discrete series representations of those groups.

The first author was supported by a National Research Foundation of Korea (NRF) grant funded by the Korean government (MSIP) (No. 2017R1C1B2010081). The second author was supported by the Croatian Science Foundation under project 9364.

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

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   54.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Hardcover Book
USD   69.99
Price excludes VAT (USA)
  • Durable hardcover 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

Learn about institutional subscriptions

References

  1. D. Ban, Parabolic induction and Jacquet modules of representations of O(2n, F). Glas. Mat. Ser. III 34(54) 2, 147–185 (1999)

    Google Scholar 

  2. J. Bernstein, A.V. Zelevinsky, Induced representations of reductive p-adic groups I. Ann. Sci. \(\acute{\text{E}}\)cole Norm. Sup. 10, 4411–472 (1977)

    Google Scholar 

  3. M. Hanzer, G. Muić, Parabolic induction and Jacquet functors for metaplectic groups. J. Algebra 323, 241–260 (2010)

    Article  MathSciNet  Google Scholar 

  4. C. Jantzen, Jacquet modules of induced representations for \(p\)-adic special orthogonal groups. J. Algebra 305, 802–819 (2006)

    Article  MathSciNet  Google Scholar 

  5. Y. Kim, Strongly positive representations of \(GSpin_2n+1\) and the Jacquet module method. with an appendix, “Strongly positive representations in an exceptional rank-one reducibility case” by Ivan Matic. Math. Z. 279, 271–296 (2015)

    Google Scholar 

  6. Y. Kim, Strongly positive representations of even \(GSpin\) groups. Pacific J. Math. 280, 69–88 (2016)

    Article  MathSciNet  Google Scholar 

  7. Y. Kim, I. Matić, Discrete series of odd \(GSpin\) groups. Preprint, available at arXiv:1706.01111

  8. I. Matić, Strongly positive representations of metaplectic groups. J. Algebra 334, 255–274 (2011)

    Article  MathSciNet  Google Scholar 

  9. I. Matić, Jacquet modules of strongly positive representations of the metaplectic groups. Trans. Amer. Math. Soc. 365(5), 2755–2788 (2013)

    Article  MathSciNet  Google Scholar 

  10. I. Matić, M. Tadić, On Jacquet modules of representations segment type. Manuscripta Math. 147, 437–476 (2015)

    Article  MathSciNet  Google Scholar 

  11. C. Mœglin, Sur la classification des séries discrètes des groupes classiques \(p\)-adiques: paramètres de Langlands et exhaustivité. J. Eur. Math. Soc. 4, 143–200 (2002)

    Article  MathSciNet  Google Scholar 

  12. C. Mœglin, M. Tadić, Construction of discrete series for classical groups. J. Am. Math. Soc. 15, 715–786 (2002)

    Article  MathSciNet  Google Scholar 

  13. A. Silberger, Special representations of reductive \(p\)-adic groups are not integrable. Ann. of Math. 111, 571–587 (1980)

    Article  MathSciNet  Google Scholar 

  14. M. Tadić, Structure arising from induction and Jacquet modules of representations of classical \(p\)-adic groups. J. Algebra 177, 1–33 (1995)

    Article  MathSciNet  Google Scholar 

  15. M. Tadić, On reducibility of parabolic induction. Israel J. Math. 107, 29–91 (1998)

    Article  MathSciNet  Google Scholar 

  16. M. Tadić, On regular square integrable representations of \(p\)-adic groups. Amer. J. Math. 120, 159–210 (1998)

    Article  MathSciNet  Google Scholar 

  17. A.V. Zelevinsky, Induced representations of reductive \(p\)-adic groups. II. On irreducible representations of GL(n)

    Google Scholar 

Download references

Acknowledgements

The first author would like to thank the organizers of the workshop on Representation theory of p-adic groups at IISER Pune, Professors Anne-Marie Aubert, Manish Mishra, Alan Roche, Steven Spallone for their invitation and hospitality. The authors would also like to thank the referee for his/her careful reading of the paper and for helpful comments and suggestions.

Author information

Authors and Affiliations

  1. Department of Mathematics Education, Chonnam National University, Yongbong-ro 77, Gwangju City, Korea

    Yeansu Kim

  2. Department of Mathematics, University of Osijek, Trg Ljudevita Gaja 6, Osijek, Croatia

    Ivan Matić

Authors
  1. Yeansu Kim
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Ivan Matić
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Yeansu Kim .

Editor information

Editors and Affiliations

  1. Institut de Mathématiques de Jussieu, Paris, France

    Anne-Marie Aubert

  2. Department of Mathematics, Indian Institute of Science Education and Research Pune, Pune, Maharashtra, India

    Manish Mishra

  3. Department of Mathematics, University of Oklahoma, Norman, OK, USA

    Alan Roche

  4. Department of Mathematics, Indian Institute of Science Education and Research Pune, Pune, Maharashtra, India

    Steven Spallone

Rights and permissions

Reprints and permissions

Copyright information

© 2019 Springer Nature Singapore Pte Ltd.

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Kim, Y., Matić, I. (2019). Classification of Strongly Positive Representations of Even General Unitary Groups. In: Aubert, AM., Mishra, M., Roche, A., Spallone, S. (eds) Representations of Reductive p-adic Groups. Progress in Mathematics, vol 328. Birkhäuser, Singapore. https://doi.org/10.1007/978-981-13-6628-4_5

Download citation

Publish with us

Policies and ethics

Search

Navigation