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Communications in Algebra Volume 31, 2003 - Issue 5
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Original Articles

Irreducibility of Certain Universal Holomorphic Harish-Chandra Modules

Dominic Lanphier Department of Mathematics, Oklahoma State University, Stillwater, Oklahoma, USA; Department of Mathematics, Oklahoma State University, Stillwater, OK, 74078-0613, USACorrespondence[email protected]
Pages 2417-2423 | Received 05 Feb 2002, Published online: 11 Dec 2006
 
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Abstract

We give a short proof of the irreducibility of Harish-Chandra modules of sufficiently high highest weight of the lowest K-type for the groups Sp n (ℝ) and U( p, q). The proof uses the action of the Casimir operator on holomorphic highest weight vectors and elementary inequalities.

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