Cohomological Representations and Functorial Transfer from Classical Groups
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.
KeywordsCohomological representations Langlands functoriality
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.
- 1.Bhagwat, C., Raghuram, A.: Endoscopy and Cohomology. Bull. Iranian Math. Soc. 43(4), 317–335 (2017)Google Scholar
- 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.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
- 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.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
- 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.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