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The Langlands Correspondence on the Generic Irreducible Constituents of Principal Series

Part of: Lie groups

Published online by Cambridge University Press:  20 November 2018

Wentang Kuo
Wentang Kuo*
Affiliation:
Department of Pure Mathematics, Faculty of Mathematics, University of Waterloo, Waterloo, ON N2L 3G1, e-mail: [email protected]
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Abstract

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Let $G$ be a connected semisimple split group over a $p$-adic field. We establish the explicit link between principal nilpotent orbits and the irreducible constituents of principal series in terms of $L$-group objects.

Keywords

Langlands correspondencenilpotent orbitsprincipal series

MSC classification

Secondary: 22E50: Representations of Lie and linear algebraic groups over local fields 22E35: Analysis on $p$-adic Lie groups
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 62 , Issue 1 , 01 February 2010 , pp. 94 - 108
Copyright
Copyright © Canadian Mathematical Society 2010

References

[1] J., Adams, D., Barbasch, and D., Vogan, The Langlands Classification and Irreducible Characters for Real Reductive Groups. Progress in Mathematics 104. Birkhäuser Boston, Boston, 1992.Google Scholar
[2] J., Adams, and D., Vogan, L-groups, projective representations, and the Langlands classification. Amer. J. Math. 114(1992), no. 1, 45-138. doi:10.2307/2374739Google Scholar
[3] A., Borel, Automorphic L-functions. In: Automorphic Forms, Representations and L-functions. Proc. Sympos. Pure Math. 33, Part 2. American Mathematical Society, Providence, RI, 1979, pp. 27-61.Google Scholar
[4] S. S., Gelbart and A.W. Knapp, L-indistinguishability and R groups for the special linear group. Adv. in Math. 43(1982), no. 2, 101-121. doi:10.1016/0001-8708(82)90030-5Google Scholar
[5] D., Kazhdan, and G., Lusztig, Proof of the Deligne-Langlands conjecture for Hecke algebras. Invent. Math. 87(1987), no. 1, 153-215. doi:10.1007/BF01389157Google Scholar
[6] C. D., Keys, On the decomposition of reducible principal series representations of p-adic Chevalley Groups. Pacific J. Math. 101(1982), no. 2, 351-388.Google Scholar
[7] C. D., Keys, L-indistinguishability and R-groups for quasisplit groups: unitary groups in even dimension. Ann. Sci. ´Ecole Norm. Sup. 20(1987), no. 1, 31-64.Google Scholar
[8] C. D., Keys and F., Shahidi, Artin L-functions and normalization of intertwining operators. Ann. Sci. École Norm. Sup. 21(1988), no. 1, 67-89.Google Scholar
[9] R., Kottwitz, Stable trace formula: cuspidal tempered terms. Duke Math. J. 51(1984), no. 3, 611-650. doi:10.1215/S0012-7094-84-05129-9Google Scholar
[10] W., Kuo, Principal nilpotent orbits and reducible principal series. Represent. Theory 6(2002), 127-159 (electronic). doi:10.1090/S1088-4165-02-00132-2Google Scholar
[11] R. P., Langlands, Representations of abelian algebraic groups. http://www.sunsite.ubc.ca/Digital MathArchive/Langlands/pdf/AbelianAlg-ps/pdf.Google Scholar
[12] R. P., Langlands, Les débuts d'une formule des traces stables, http://www.sunsite.ubc.ca/Digital MathArchive/Langlands/pdf/traces-ps/pdf.Google Scholar
[13] G., Lusztig, Classification of unipotent representations of semisimple p-adic groups. Internat. Math. Res. Notices 1995, no. 11, 517-589.Google Scholar
[14] J. S., Milne, Arithmetic Duality Theorems. Perspectives in Mathematics 1. Academic Press, Boston, 1986.Google Scholar
[15] T. A., Springer, Reductive groups, in Automorphic Forms, Representations and L-functions. Proc. Symp. Pure Math. 33, Part 1. American Mathematical Society, Providence, RI, 1979, pGoogle Scholar
[16] T. A., Springer, Linear Algebraic Groups. Second edition. Birkhäuser Boston, Boston, 1998.Google Scholar