Details

Subject(s)

• Semisimple Lie groups [Browse]
• Representations of groups [Browse]

Series

• Memoirs of the American Mathematical Society ; no. 216. [More in this series]
• Memoirs of the American Mathematical Society, 0065-9266 ; no. 216 [More in this series]

Summary note

Non-spherical principal series representations of a real semisimple Lie group are studied. These are representations, induced by a one-dimensional representation of a minimal parabolic subgroup, which have a one-dimensional subspace left stable by a maximal compact subgroup of the original group G. Necessary and sufficient conditions for such a representation to be irreducible, or to be cyclic, are found, in terms of parameters determined by certain rank one subgroups of G. A sufficient condition for such a representation to be unitary is found, and the condition is shown to be necessary in the rank one case

Notes

"Volume 19 ... (first of 2 numbers)."

Bibliographic references

Bibliography: p. 51-52.

Contents

• Introduction
• Chapter I: Section 1.
• Definitions and Major Results
• Section 2. An Outline
• Chapter II: Section 3. Preliminaries
• Section 4. The Irreducible Modules z[
• Section 5. Irreducibility and Cyclicity
• Section 6. Unitarity
• Section 7. An Expression for R^ 23
• Chapter III: Section 8. Reduction to Rank One
• Section 9. The Rank One Case
• Section 10. The Diagonal Map
• Section 11. Finite Dimensional Representations
• Section 12. Calculating p^ for su(N,l)
• Chapter IV: Section 13.
• The Zeros of R^ and P^
• Section 14. Representations of the Group GQ
• Section 15. An Application
• Bibliography
• An Outline
• Preliminaries
• The Irreducible Modules Z γ τ
• Irreducibility and Cyclicity
• Unitarity
• An Expression for R γ τ
• Reduction to Rank One
• The Rank One Case The Diagonal Map
• Finite Dimensional Reresentations
• Calculating p τ γ for su )N,1)
• The Zeros of R γ τ and P γ τ
• Representations of the Group G O
• An Application

Show 29 more Contents items

ISBN

• 0821822160
• 9780821822166

LCCN

79010157

OCLC

4775805

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