Skip to main content
SpringerLink
Log in

The degenerate principal series representations of exceptional groups of type E6 over p-adic fields

  • Published:
Israel Journal of Mathematics Aims and scope Submit manuscript

    We’re sorry, something doesn't seem to be working properly.

    Please try refreshing the page. If that doesn't work, please contact support so we can address the problem.

Abstract

In this paper, we study the reducibility of degenerate principal series of the simple, simply-connected exceptional group of type E6. Furthermore, we calculate the maximal semi-simple subrepresentation and quotient of these representations.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. M. Asgari, Local L-functions for split spinor groups, Canadian Journal of Mathematics 54 (2002), 673–693.

    Article  MathSciNet  Google Scholar 

  2. D. Ban and C. Jantzen, Degenerate principal series for even-orthogonal groups, Representation Theory 7 (2003), 440–480.

    Article  MathSciNet  Google Scholar 

  3. D. Ban and C. Jantzen, Jacquet modules and the Langlands classification, Michigan Mathematical Journal 56 (2008), 637–653.

    Article  MathSciNet  Google Scholar 

  4. I. N. Bernšteĭn and A. V. Zelevinskiĭ, Representations of the group GL(n, F), where F is a local non-Archimedean field, Uspekhi Matematicheskikh Nauk 31 (1976), 5–70.

    MathSciNet  MATH  Google Scholar 

  5. I. N. Bernstein and A. V. Zelevinsky, Induced representations of reductive p-adic groups. I, Annales Scientifiques de l’´Ecole Normale Supérieure 10 (1977), 441–472.

    Article  MathSciNet  Google Scholar 

  6. W. Casselman, Introduction to the theory of admissible representations of p-adic reductive groups, http://www.math.ubc.ca/~cass/research/pdf/p-adic-book.pdf.

  7. S. Choi and C. Jantzen, Degenerate principal series for the exceptional p-adic groups of type F4, Journal of Lie Theory 20 (2010), 785–806.

    MathSciNet  MATH  Google Scholar 

  8. W. T. Gan and G. Savin, A family of arthur packets of triality spin(8), Unpublished.

  9. S. S. Gelbart and A. W. Knapp, Irreducible constituents of principal series of SLn(k), Duke Mathematical Journal 48 (1981), 313–326.

    Article  MathSciNet  Google Scholar 

  10. H. Halawi, Poles of degenerate Eisenstein series and Siegel–Weil identities for exceptional split groups, Master’s thesis, Ben-Gurion University, 2016.

    Google Scholar 

  11. C. Jantzen, Degenerate principal series for symplectic groups, Memoirs of the American Mathematical Society 102 (1993).

    Article  MathSciNet  Google Scholar 

  12. C. Jantzen, On the Iwahori–Matsumoto involution and applications, Annales Scientifiques de l’´Ecole Normale Supérieure 28 (1995), 527–547.

    Article  MathSciNet  Google Scholar 

  13. C. Jantzen, Degenerate principal series for symplectic and odd-orthogonal groups, Memoirs of the American Mathematical Society 124 (1996).

    Article  MathSciNet  Google Scholar 

  14. M. A. A. van Leeuwen, A. M. Cohen and B. Lisser, Lie: a Package for Lie Group Computations, Centrum voor Wiskunde en Informatica, Amsterdam, 1992.

    Google Scholar 

  15. G. Mui´c, The unitary dual of p-adic G2, Duke Mathematical Journal 90 (1997), 465–493.

    Article  MathSciNet  Google Scholar 

  16. A. Segal, The degenerate residual spectrum of quasi-split forms of Spin8 associated to the Heisenberg parabolic subgroup, Transactions of the American Mathematical Society 372 (2019), 6703–6754.

    Article  MathSciNet  Google Scholar 

  17. A. Segal, Survey on the principal series representations of GLn for small n, Unpublished.

  18. R. Steinberg, Lectures on Chevalley Groups, Yale University, New Haven, CT, 1968.

    MATH  Google Scholar 

  19. M. Tadi´c, Notes on representations of non-Archimedean SL(n), Pacific Journal of Mathematics 152 (1992), 375–396.

    Article  MathSciNet  Google Scholar 

  20. M. Tadi´c, On reducibility of parabolic induction, Israel Journal of Mathematics 107 (1998), 29–91.

    Article  MathSciNet  Google Scholar 

  21. The Sage Developers, Sagemath, the Sage Mathematics Software System (Version x.y.z), http://www.sagemath.org.

  22. M. H. Weissman, The Fourier–Jacobi map and small representations, Representation Theory 7 (2003), 275–299.

    Article  MathSciNet  Google Scholar 

  23. A. V. Zelevinsky, Induced representations of reductive p-adic groups. II. On irreducible representations of GL(n), Annales Scientifiques de l’´Ecole Normale Supérieure 13 (1980), 165–210.

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Mathematics, Ben Gurion University of the Negev, POB 653, Be’er Sheva, 84105, Israel

    Hezi Halawi

  2. Department of Mathematics, University of British Columbia, Vancouver, BC, V6T 1Z2, Canada

    Avner Segal

  3. Department of Mathematics, Bar Ilan University, Ramat Gan, 5290002, Israel

    Avner Segal

Authors
  1. Hezi Halawi
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Avner Segal
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Avner Segal.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Halawi, H., Segal, A. The degenerate principal series representations of exceptional groups of type E6 over p-adic fields. Isr. J. Math. 238, 537–569 (2020). https://doi.org/10.1007/s11856-020-2015-y

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11856-020-2015-y

Search

Navigation