Poisson transforms on vector bundles
Author:
An Yang
Journal:
Trans. Amer. Math. Soc. 350 (1998), 857-887
MSC (1991):
Primary 22E46; Secondary 43A85
DOI:
https://doi.org/10.1090/S0002-9947-98-01659-6
MathSciNet review:
1370656
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Abstract | References | Similar Articles | Additional Information
Abstract: Let be a connected real semisimple Lie group with finite center, and
a maximal compact subgroup of
. Let
be an irreducible unitary representation of
, and
the associated vector bundle. In the algebra of invariant differential operators on
the center of the universal enveloping algebra of
induces a certain commutative subalgebra
. We are able to determine the characters of
. Given such a character we define a Poisson transform from certain principal series representations to the corresponding space of joint eigensections. We prove that for most of the characters this map is a bijection, generalizing a famous conjecture by Helgason which corresponds to
the trivial representation.
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Additional Information
An Yang
Affiliation:
Department of Mathematics, Massachusetts Institute of Technology, 2-251, Cambridge, Massachusetts 02139
Address at time of publication:
Micro Strategy, 5th Floor, 2650 Park Tower Dr., Metro Place 1, Vienna, Virginia 22180
Email:
yang@strategy.com
DOI:
https://doi.org/10.1090/S0002-9947-98-01659-6
Received by editor(s):
September 28, 1994
Received by editor(s) in revised form:
January 30, 1995
Article copyright:
© Copyright 1998
American Mathematical Society