Discrete decomposability of the restriction of Aq(λ) with respect to reductive subgroups
III. Restriction of Harish-Chandra modules and associated varieties |
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Authors: | Toshiyuki Kobayashi |
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Institution: | (1) Department of Mathematical Sciences, University of Tokyo, Meguro, Komaba, 153, Tokyo, Japan (e-mail: toshi@ms.u-tokyo.ac.jp), JP |
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Abstract: | Let H⊂G be real reductive Lie groups and π an irreducible unitary representation of G. We introduce an algebraic formulation (discretely decomposable restriction) to single out the nice class of the branching
problem (breaking symmetry in physics) in the sense that there is no continuous spectrum in the irreducible decomposition
of the restriction π|
H
. This paper offers basic algebraic properties of discretely decomposable restrictions, especially for a reductive symmetric
pair (G,H) and for the Zuckerman-Vogan derived functor module , and proves that the sufficient condition Invent. Math. '94] is in fact necessary. A finite multiplicity theorem is established
for discretely decomposable modules which is in sharp contrast to known examples of the continuous spectrum. An application
to the restriction π|
H
of discrete series π for a symmetric space G/H is also given.
Oblatum 2-X-1996 & 10-III-1997 |
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Keywords: | |
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