Vol. 260, No. 2, 2012

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Some comments on Weyl’s complete reducibility theorem

Jonathan Rogawski and V. S. Varadarajan

Vol. 260 (2012), No. 2, 687–694
Abstract

In this note we discuss a purely algebraic proof of Weyl’s theorem that all finite-dimensional representations of a complex semisimple Lie algebra are completely reducible. We give a simple and direct proof which is elementary in the sense that it does not use cohomology, and which is a synthesis of the older proofs of Casimir – van der Waerden and of Brauer.

Keywords
Weyl’s reducibility theorem
Mathematical Subject Classification 2010
Primary: 17B20, 22E46
Milestones
Received: 16 July 2012
Accepted: 22 July 2012
Published: 30 November 2012
Authors
Jonathan Rogawski
Department of Mathematics
University of California, Los Angeles
Los Angeles, CA 90095
United States
V. S. Varadarajan
Department of Mathematics
University of California, Los Angeles
Los Angeles, CA 90095
United States