Glasnik Matematicki, Vol. 45, No.2 (2010), 373-393.

THE SMOOTH IRREDUCIBLE REPRESENTATIONS OF U(2)

Manouchehr Misaghian

Department of Mathematics, Prairie View A & M University, Prairie View, TX 77446
e-mail: mamisaghian@pvamu.edu


Abstract.   In this paper we parametrize all smooth irreducible representations of U(2), the compact unitary group in two variables.

2000 Mathematics Subject Classification.   11F27, 20E99, 22E50.

Key words and phrases.   Group of isometries, stabilizer, smooth representation, induction.


Full text (PDF) (free access)

DOI: 10.3336/gm.45.2.06


References:

  1. C. Curtis, I. Reiner, Representation theory and associative algebra, Wiley, New York, 1988.
    MathSciNet    

  2. J. Dieudonné, La géométrie des groupes classiques, Second édition, Springer-Verlag, Berlin, 1963.
    MathSciNet    

  3. I. B. Fesenko, S. Vostokov, Local fields and their extensions, AMS, Rhode Island, 1993.
    MathSciNet    

  4. P. Kutzko, On the supercuspidal representations of Gl2 II, Amer. J. Math. 100 (1978), 705-716.

  5. D. Manderscheid, On the supercuspidal representations of SL2 and its two-fold cover. II, Math. Ann. 266 (1984), 287-295.
    MathSciNet     CrossRef

  6. D. Manderscheid, Supercuspidal representations and the theta correspondence II: SL(2) and The Anisotropic O(3), Trans. Amer. Math. Soc., 336 (1993), 805-816.
    MathSciNet     CrossRef

  7. M. Misaghian, Representations of D1, Rocky Mountain J. Math. 35 (2005), 953-976.
    MathSciNet     CrossRef

  8. O. O'Meara, Introduction to quadratic forms, Springer-Verlag, New York, 1971.
    MathSciNet    

  9. I. Reiner, Maximal orders, Academic Press, London 1975.
    MathSciNet    

  10. Marie-France Vignéras, Arithmétique des algèbres de quaternions, Springer-Verlag, Berlin Heidelberg New York, 1980.
    MathSciNet    

  11. C. Moeglin, M.-F. Vignéras, J.-L. Waldspurger, Correspondances de Howe sur un corps p-adique, Lecture Notes in Math. 1291, Springer-Verlag, Berlin/New York, 1987.
    MathSciNet    

  12. S. Stevens, Intertwining and supercuspidal types for p-adic classical groups, Proc. London Math. Soc. (3) 83 (2001), 120-140.
    MathSciNet     CrossRef

  13. A. Weil, Basic number theory, Springer-Verlag, New York, 1967.
    MathSciNet    

  14. E. Weiss, Algebraic number theory, Mc Graw-Hill Book Company, New York, 1963.
    MathSciNet    

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