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Classification of Irreducible Tempered Representations of Semisimple Lie Groups

A. W. Knapp and Gregg Zuckerman
Proceedings of the National Academy of Sciences of the United States of America
Vol. 73, No. 7 (Jul., 1976), pp. 2178-2180
Stable URL: http://www.jstor.org/stable/65732
Page Count: 3
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Classification of Irreducible Tempered Representations of Semisimple Lie Groups
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Abstract

For each connected real semisimple matrix group, one obtains a constructive list of the irreducible tempered unitary representations and their characters. These irreducible representations all turn out to be instances of a more general kind of representation, here called basic. The result completes Langlands's classification of all irreducible admissible representations for such groups. Since not all basic representations are irreducible, a study is made of character identities relating different basic representations and of the commuting algebra for each basic representation.

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