Derived intertwining norms for reducible spherical principal series

J. E. Gilbert*, R. A. Kunze, C. Meaney

*Corresponding author for this work

    Research output: Contribution to journalArticlepeer-review


    We use the second derivative of intertwining operators to realize a unitary structure for the irreducible subrepresentations in the reducible spherical principal series of U (1, n). These representations can also be realized as the kernels of certain invariant first-order differential operators acting on sections of homogeneous bundles over the hyperboloid (U(1) × U(n))\U(1, n).

    Original languageEnglish
    Pages (from-to)171-188
    Number of pages18
    JournalJournal of the Australian Mathematical Society
    Issue number2
    Publication statusPublished - Oct 1996


    • Cauchy-Szegö map
    • Intertwining operator
    • Jantzen filtration
    • Principal series
    • Real rank one semisimple Lie group


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