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On the composition series of principal series representations of a three-fold covering group of SL(2, K)1)

Published online by Cambridge University Press:  22 January 2016

Haluk Aritürk
Haluk Aritürk*
Affiliation:
Bogazici University, P.K. 2, Bebek Istanbul, Turkey
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In this paper, we study the composition series of certain principal series representations of the three-fold metaplectic covering group of SL(2, K), where K is a non-archimedean local field. These representations are parametrized by unramified characters μ(x) = |x|s of K× and characters ω of the group of third roots of unity.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 77 , February 1980 , pp. 177 - 196
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1980

Footnotes

1)

This work was partially supported by the Scientific and Technical Research Council of Turkey.

References

[1] Artin, E. and Tate, J., Class Field Theory, W.A. Benjamin, New York, 1968.Google Scholar
[2] Casselman, W., Some general results in the theory of admissable representations of P-adic reductive groups, to appear.Google Scholar
[3] Gelbart, S., Weil’s representation and the spectrum of the metaplectic groups, Lecture Notes in Mathematics, No. 530, Springer-Verlag, 1976.Google Scholar
[4] Gelbart, S. and Sally, P. J., Intertwining operators and automorphic forms on the metaplectic group, Proc. Nat. Acad. Sci., USA, 72 (1975), 1406–1410.CrossRefGoogle Scholar
[5] Godement, R., Notes on Jacquet-Langlands Theory, Institute for Advanced Study, Princeton, 1970.Google Scholar
[6] Jacquet, H. and Langlands, R. P., Automorphic forms on GL(2), Lecture Notes in Mathematics, No. 114, Springer-Verlag, 1970.CrossRefGoogle Scholar
[7] Kubota, T., Automorphic functions and the reciprocity law in a number field, Kyoto University, 1969.Google Scholar
[8] Langlands, R. P., On the classification of irreducible representations of real reductive groups, Mimeographed notes, Institute for Advanced Study, 1973.Google Scholar
[9] Sally, P. J. and Taibleson, M. H., Special functions on locally compact fields, Acta Mathematica, 116 (1966), 279–309.CrossRefGoogle Scholar