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The Pushpa Publishing House proposes to organize a five day "International Conference on Mathematics of Date" from December 31, 2010 to January 04, 2011 scheduled to be held at Allahabad, India.

 
  JP Journal of Geometry and Topology  
 ISSN: 0972-415X
 
 
 

     JP Journal of Geometry and Topology
    Volume 9, Issue 3, Pages 249 - 262 (November 2009)


REMARKS ON THE PRINCIPAL SERIES OF REPRESENTATIONS: THE CASE OF

U. N. Bassey and O. O. Oyadare

Received April 4, 2009

References:



[1] W. H. Baker, harmonic analysis on Mem. Amer. Math. Soc. 76 (1988), 110 pp.

[2] U. N. Bassey and O. O. Oyadare, Basic theorems about harmonic analysis of spherical functions on Contemporary Problems in Mathematical Physics (COPROMAPH) 5 (2008), 240-252.

[3] Harish-Chandra, Plancherel formula for the real unimodular group, Proc. Nat. Acad. Sci. U. S. A. 38 (1952), 337-342.

[4] Harish-Chandra, Harmonic analysis on semisimple Lie groups, Bull. Amer. Math. Soc. 76 (1970), 529-551.

[5] S. Helgason, Differential Geometry and Symmetric Spaces, Academic Press, New York, London, 1962.

[6] S. Helgason, A duality for symmetric spaces with applications to group representations, Adv. Math. 5 (1970), 1-154.

[7] R. A. Herb, Weighted orbital integrals on Mém. Soc. Math. France (N.S.) 15 (1984), 201-217.

[8] A. W. Knapp, Determination of intertwining operators, Harmonic Analysis on Homogeneous Spaces, Proc. Sympos. Pure Math., Vol. XXVI, Williams Coll., Williamstown, Mass., 1972, pp. 263-268, Amer. Math. Soc., Providence, R.I, 1973.

[9] A. W. Knapp and E. M. Stein, Intertwining operators for semisimple groups, Ann. of Math. (2) 93 (1971), 489-578.

[10] A. W. Knapp and P. E. Trapa, Representations of Semisimple Lie Groups, IAS/Park City Mathematics Series, 8, 1998, pp. 7-87.

[11] B. Kostant, On the existence and irreducibility of certain series of representations, Bull. Amer. Math. Soc. 75 (1969), 627-642.

[12] R. A. Kunze and E. M. Stein, Uniformly bounded representations. III. Intertwining operators for the principal series on semisimple groups, Amer. J. Math. 89 (1967), 385-442.

[13] R. L. Lipsman, Group representations, Lecture Notes in Mathematics 388, Springer-Verlag, Berlin, New York, 1974.

[14] O. O. Oyadare, Harmonic analysis of spherical functions on Unpublished M.Sc. Research, University of Ibadan, Nigeria, 2007.

[15] R. R. Rao, Unitary representations defined by boundary conditions - the case of Acta Math. 139 (1977), 185-216.

[16] L. P. Rothschild, Invariant polynomials and conjugacy classes of real Cartan subalgebras, Bull. Amer. Math. Soc. 77 (1971), 762-764.

[17] P. J. Sally, Jr. and G. Warner, The Fourier transforms on semisimple Lie groups of real rank one, Acta Math. 131 (1973), 1-26.

[18] G. Schiffmann, Intégrales d’entrelacement et fonctions de Whittaker, Bull. Soc. Math. France 99 (1971), 3-72 (in French).

[19] V. S. Varadarajan, An Introduction to Harmonic Analysis on Semisimple Lie Groups, Cambridge University Press, Cambridge, 1989.

[20] G. Warner, Harmonic Analysis on Semisimple Lie Groups, Vols. I and II, Springer, Berlin, 1972.

[21] J. A. Wolf, Foundations of representation theory for semisimple Lie groups, Harmonic Analysis and Representations of Semisimple Lie Groups, D. Riedel, 1980.

Keywords and phrases: cocycles, parabolic induction, principal series, representations,

Communicated by Yasuo Matsushita

 


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