Advertisement

Cohomological Representations and Functorial Transfer from Classical Groups

  • A. RaghuramEmail author
  • Makarand Sarnobat
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 245)

Abstract

We study whether the property of being cohomological is preserved under Langlands functoriality for the transfer of tempered representations from real classical Lie groups to an appropriate general linear group.

Keywords

Cohomological representations Langlands functoriality 

Notes

Acknowledgements

We thank Dipendra Prasad for his interest in the results of this project, and for helpful tutorials on Langlands parameters. We also thank the referee for a very careful reading and helpful comments.

References

  1. 1.
    Bhagwat, C., Raghuram, A.: Endoscopy and Cohomology. Bull. Iranian Math. Soc. 43(4), 317–335 (2017)Google Scholar
  2. 2.
    Borel, A.: Automorphic L-functions, Automorphic forms, Representations and L-functions (Proceedings of Symposia in Pure Mathematics, Oregon State University, Corvallis, Oregon, 1977), Part 2, XXXIII, pp. 27–61. American Mathematical Society, Providence (1979)Google Scholar
  3. 3.
    Borel, A., Wallach, N.: Continuous Cohomology, Discrete Subgroups and Representations of Reductive Groups. Mathematical Surveys and Monographs, vol. 67, 2nd edn, xviii+260 pp. American Mathematical Society, Providence (2000). ISBN: 0-8218-0851-6Google Scholar
  4. 4.
    Gross, B.H., Reeder, M.: From Laplace to Langlands via representations of orthogonal groups. Bull. Am. Math. Soc. (N.S.) 43(2), 163–205 (2006)MathSciNetCrossRefGoogle Scholar
  5. 5.
    Kim, H.H., Krishnamurthy, M.: Stable base change lift from unitary groups to GL\((n)\). IMRP Int. Math. Res. Pap. 1, 1–52 (2005)Google Scholar
  6. 6.
    Knapp, A.: Local Langlands Correspondence - The Archemedean case, Motives. Proceedings in Symposia of Pure Mathematics, vol. 55, Part II, pp. 393–410. Seattle, WA 1991 (1994)Google Scholar
  7. 7.
    Labesse, J.-P., Schwermer, J.: On liftings and cusp cohomology of arithmetic groups. Invent. Math. 83, 383–401 (1986)MathSciNetCrossRefGoogle Scholar
  8. 8.
    Langlands, R.P.: On the classification of irreducible representations of real algebraic groups. Representation Theory and Harmonic Analysis on Semi-Simple Lie Groups. Mathematical Surveys and Monographs, vol. 31, pp. 101–170. American Mathematical Society, Providence (1989)CrossRefGoogle Scholar
  9. 9.
    Raghuram, A.: Critical values of Rankin-Selberg L-functions for GL\((n) \times GL(n-1)\) and the symmetric cube L-functions for GL\((2)\). Forum Math. 28(3), 457–489 (2016)Google Scholar
  10. 10.
    Raghuram, A., Shahidi, F.: Funtoriality and special values of L-functions. In: Gan, W.T., Kudla, S., Tschinkel, Y. (eds.) Eisenstein Series and Applications. Progress in Mathematics, vol. 258, pp. 271–294. Birkhäuser Boston, Boston (2008)Google Scholar

Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Indian Institute of Science Education and ResearchPashan, PuneIndia

Personalised recommendations