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The Weyl character formula, the half-spin representations, and equal rank subgroups. (English) Zbl 0918.17002

Summary: Let \(B\) be a reductive Lie subalgebra of a semisimple Lie algebra \(F\) of the same rank both over the complex numbers. To each finite dimensional irreducible representation \(V_\lambda\) of \(F\) the authors assign a multiplet of irreducible representations of \(B\) with \(m\) elements in each multiplet, where \(m\) is the index of the Weyl group of \(B\) in the Weyl group of \(F\). They obtain a generalization of the Weyl character formula; their formula gives the character of \(V_\lambda\) as a quotient whose numerator is an alternating sum of the characters in the multiplet associated to \(V_\lambda\) and whose denominator is an alternating sum of the characters of the multiplet associated to the trivial representation of \(F\).

MSC:

17B10 Representations of Lie algebras and Lie superalgebras, algebraic theory (weights)
17B20 Simple, semisimple, reductive (super)algebras
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