The Langlands Classification and Irreducible Characters for Real Reductive Groups

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Birkhäuser Boston, May 1, 1992 - Mathematics - 320 pages
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IIunit(G(R)) :::> IItemp(G(R)) (1. 1) to be the set ofequivalence classes ofirreducible admissible (respectively unitary or tempered) representations of G(R). Now define (G(R)) :::> temp(G(R)) (1. 2) to be the set ofLanglands parameters for irreducible admissible (respec tively tempered) representations of G(R) (see [34], [10], [1]' Chapter 5, and Definition 22. 3). To each ¢ E (G(R)), Langlands attaches a finite set II C II(G(R)), called an L-packet of representations. The L-packets II partition II(G(R)). If ¢ E temp(G(R)), then the representations in II are all tempered, and in this way one gets also a partition of II (G(R)). temp Now the classification of the unitary representations of G(IR) is one of the most interesting unsolved problems in harmonic analysis.

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Douglas Adams

Douglas Adams was born in Cambridge, England in 1952. He has written for radio, television and theater and has worked as a hospital reporter, barn builder, radio producer, and script editor. His bestsellers include "The Hitchhiker's Guide to the Galaxy, the Restaurant at the End of the Universe, Life, the Universe and Everything, So Long and Thanks for All the Fish, Dirk Gently's Holistic Detective Agency, and "The Long Dark Tea-Time of the Soul.

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