Internal Multiplicity Structure and Clebsch-Gordan Series for the Exceptional Group G(2)
- 1 November 1967
- journal article
- research article
- Published by AIP Publishing in Journal of Mathematical Physics
- Vol. 8 (11), 2206-2209
- https://doi.org/10.1063/1.1705142
Abstract
An explicit algebraic formula is obtained for the multiplicity M̄(γ) of a vector γ belonging to the fundamental domain of the group G(2). Using this, the internal multiplicity Mm(m′) of a weight m′ of the irreducible representation D(m) with the highest weight m is calculated through Kostant's formula for the dominant weights. The Clebsch‐Gordan decomposition of the direct product of two irreducible representations is then obtained.Keywords
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