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Representation Theory

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Multiplicity-free products and restrictions of Weyl characters

Author: John R. Stembridge
Journal: Represent. Theory 7 (2003), 404-439
MSC (2000): Primary 17B10, 05E15; Secondary 20G05, 22E46
Published electronically: October 7, 2003
MathSciNet review: 2017064
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Abstract: We classify all multiplicity-free products of Weyl characters, or equivalently, all multiplicity-free tensor products of irreducible representations of complex semisimple Lie algebras. As a corollary, we also obtain the classification of all multiplicity-free restrictions of irreducible representations to reductive subalgebras of parabolic type.

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John R. Stembridge
Affiliation: Department of Mathematics, University of Michigan, Ann Arbor, Michigan 48109–1109

Received by editor(s): December 12, 2001
Received by editor(s) in revised form: September 22, 2003
Published electronically: October 7, 2003
Additional Notes: This work was supported by NSF Grant DMS–0070685
Article copyright: © Copyright 2003 American Mathematical Society