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 ℊℂ 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.
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© 1983 Birkhäuser Boston, Inc.
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Enright, T., Howe, R., Wallach, N. (1983). A Classification of Unitary Highest Weight Modules. In: Trombi, P.C. (eds) Representation Theory of Reductive Groups. Progress in Mathematics, vol 40. Birkhäuser Boston. https://doi.org/10.1007/978-1-4684-6730-7_7
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DOI: https://doi.org/10.1007/978-1-4684-6730-7_7
Publisher Name: Birkhäuser Boston
Print ISBN: 978-0-8176-3135-2
Online ISBN: 978-1-4684-6730-7
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