Derived intertwining norms for reducible spherical principal series

J. E. Gilbert; R. A. Kunze; C. Meaney

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 journal › Article › peer-review

Abstract

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 language	English
Pages (from-to)	171-188
Number of pages	18
Journal	Journal of the Australian Mathematical Society
Volume	61
Issue number	2
Publication status	Published - Oct 1996

Keywords

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

Cite this

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title = "Derived intertwining norms for reducible spherical principal series",

abstract = "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).",

keywords = "Cauchy-Szeg{\"o} map, Intertwining operator, Jantzen filtration, Principal series, Real rank one semisimple Lie group",

author = "Gilbert, {J. E.} and Kunze, {R. A.} and C. Meaney",

year = "1996",

month = oct,

language = "English",

volume = "61",

pages = "171--188",

journal = "Journal of the Australian Mathematical Society",

issn = "1446-7887",

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T1 - Derived intertwining norms for reducible spherical principal series

AU - Gilbert, J. E.

AU - Kunze, R. A.

AU - Meaney, C.

PY - 1996/10

Y1 - 1996/10

N2 - 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).

AB - 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).

KW - Cauchy-Szegö map

KW - Intertwining operator

KW - Jantzen filtration

KW - Principal series

KW - Real rank one semisimple Lie group

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M3 - Article

AN - SCOPUS:0041115685

SN - 1446-7887

VL - 61

SP - 171

EP - 188

JO - Journal of the Australian Mathematical Society

JF - Journal of the Australian Mathematical Society

IS - 2

ER -

Derived intertwining norms for reducible spherical principal series

Abstract

Keywords

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