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Centralizers and Twisted Centralizers: Application to Intertwining Operators

Published online by Cambridge University Press:  20 November 2018

Xiaoxiang Yu
Xiaoxiang Yu*
Affiliation:
Institute of Science, Wuhan Institute of Technology, Hubei, China e-mail: tianyuanwing@yahoo.com
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Abstract

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The equality of the centralizer and twisted centralizer is proved based on a case-by-case analysis when the unipotent radical of a maximal parabolic subgroup is abelian. Then this result is used to determine the poles of intertwining operators.

Keywords

11F70
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 58 , Issue 3 , 01 June 2006 , pp. 643 - 672
Copyright
Copyright © Canadian Mathematical Society 2006

References

[1] Goldberg, D. and Shahidi, F., On the tempered spectrum of quasi-split classical groups. Duke Math. J. 92(1998), no. 2, 255–294.Google Scholar
[2] Goldberg, D. and Shahidi, F., On the tempered spectrum of quasi-split classical groups. III. The odd orthogonal groups. Forum Math., to appearGoogle Scholar
[3] Humphreys, J., Introduction to Lie Algebras and Representation Theory. Graduate Texts in Mathematics 9, Springer-Verlag, New York, 1978.Google Scholar
[4] Muller, I., Décomposition orbitale des spaces préhomogènes réguliers de type parabolique commutatif et application. C. R. Acad. Sci Paris Sér. I Math. 303(1986), no. 11, 495–498.Google Scholar
[5] Sato, M. and Kimura, T., A classification of irreducible prehomogeneous vector spaces and their relative invariants. Nagoya Math. J. 65(1977), 1–155.Google Scholar
[6] Shahidi, F., A proof of Langlands’ conjecture on Plancherel measures: Complementary series for p-adic groups. Ann of Math. 132(1990), no. 2, 273–330.Google Scholar
[7] Shahidi, F., Twisted endoscopy and reducibility of induced representations for p-adic groups. Duke Math. J. 66(1992), no. 1, 1–41.Google Scholar
[8] Shahidi, F., Poles of intertwining operators via endoscopy; the connection with prehomogeneous vector spaces. Compositio Math. 120(2000), no. 3, 291–325.Google Scholar
[9] Shahidi, F., Local coefficients as Mellin transforms of Bessel functions: Towards a general stability. Int. Math. Res. Not. 39(2002), no. 39, 2075–2119.Google Scholar
[10] Springer, T. A., Linear Algebraic Groups. Second edition. Progress in Mathematics 126, Springer-Verlag, New York, 1991.Google Scholar
[11] Vinberg, E. B., The Weyl group of a graded Lie algebra. Izv. Akad. Nauk SSSR Ser.Mat. 40(1976), no. 3, 488–526. 709.Google Scholar