Abstract
A Lie–Poisson isomorphism for Lie algebras 𝔤 and 𝔮 =𝔨 ×𝔨 is derived in a closed form, where 𝔤 is complex and simple, and 𝔨 is the maximal compact subalgebra in 𝔤 . This isomorphism enables one to find a generalized Gell-Mann formula relating unitary irreducible representations of the corresponding Lie groups G and Q. The case 𝔤 =sl(n,C), 𝔨 =su(n) is considered in detail. A simple relation between characters is obtained.
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