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January, 2007 Multiplicity-free branching rules for outer automorphisms of simple Lie algebras
Hidehisa ALIKAWA
J. Math. Soc. Japan 59(1): 151-177 (January, 2007). DOI: 10.2969/jmsj/1180135505


We find explicit multiplicity-free branching rules of some series of irreducible finite dimensional representations of simple Lie algebras 𝔤 to the fixed point subalgebras 𝔤 σ of outer automorphisms σ . The representations have highest weights which are scalar multiples of fundamental weights or linear combinations of two scalar ones. Our list of pairs of Lie algebras ( 𝔤 , 𝔤 σ ) includes an exceptional symmetric pair ( E 6 , F 4 ) and also a non-symmetric pair ( D 4 , G 2 ) as well as a number of classical symmetric pairs. Some of the branching rules were known and others are new, but all the rules in this paper are proved by a unified method. Our key lemma is a characterization of the ``middle'' cosets of the Weyl group of 𝔤 in terms of the subalgebras 𝔤 σ on one hand, and the length function on the other hand.


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Hidehisa ALIKAWA. "Multiplicity-free branching rules for outer automorphisms of simple Lie algebras." J. Math. Soc. Japan 59 (1) 151 - 177, January, 2007.


Published: January, 2007
First available in Project Euclid: 25 May 2007

zbMATH: 1136.17005
MathSciNet: MR2302667
Digital Object Identifier: 10.2969/jmsj/1180135505

Primary: 17B10
Secondary: 05E15

Keywords: branching rule , characters of Lie groups , graph automorphism , multiplicity free , outer automorphism , Semisimple Lie groups

Rights: Copyright © 2007 Mathematical Society of Japan


Vol.59 • No. 1 • January, 2007
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