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A Classification of Unitary Highest Weight Modules

  • Thomas Enright
  • Roger Howe
  • Nolan Wallach
Part of the Progress in Mathematics book series (PM, volume 40)

Abstract

Let G be a simply connected, connected simple Lie group with center Z. Let K be a closed maximal subgroup of G with K/Z compact and let g be the Lie algebra of G. A unitary representation (π,H) of G such that the underlying (ℊK) — module is an irreducible quotient of a Verma module for ℊ is called a unitary highest weight module. Harish-Chandra ([4],[5]) has shown that G admits nontrivial unitary highest weight modules precisely when (G,K) is a Hermitian symmetric pair. In this paper we give a complete classification of the unitary highest weight modules.

Keywords

Root System Simple Root Verma Module Trivial Representation High Weight Vector 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Birkhäuser Boston, Inc. 1983

Authors and Affiliations

  • Thomas Enright
  • Roger Howe
  • Nolan Wallach

There are no affiliations available

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