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On Gelfand-Zetlin modules

Drozd, Yu. A.Ovsienko, S. A.Futorny, V. M. — 1991

Proceedings of the Winter School "Geometry and Physics"

[For the entire collection see Zbl 0742.00067.]Let 𝔤 k be the Lie algebra 𝔤 l ( k , 𝒞 ) , and let U k be the universal enveloping algebra for 𝔤 k . Let Z k be the center of U k . The authors consider the chain of Lie algebras 𝔤 n 𝔤 n - 1 𝔤 1 . Then Z = Z k k = 1 , 2 , n is an associative algebra which is called the Gel’fand-Zetlin subalgebra of U n . A 𝔤 n module V is called a G Z -module if V = x V ( x ) , where the summation is over the space of characters of Z and V ( x ) = { v V ( a - x ( a ) ) m v = 0 , m 𝒵 + , a 𝒵 } . The authors describe several properties of G Z - modules. For example, they prove that if V ( x ) = 0 for some x ...

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