= Gelfand–Tsetlin algebra
{c}
{title2=$GZ_n$}
= Gelfand–Tsetlin subalgebra
{c}
{synonym}
= Gelfand–Tzetlin algebra
{c}
{synonym}
For the chain $S_0\subset\cdots\subset S_n$, the Gelfand–Tsetlin algebra in $\mathbb C S_n$ is generated by the centers of $\mathbb C S_r$ for $0\leq r\leq n$. <Multiplicity-free restriction> makes its joint eigenspaces one-dimensional in each <irreducible representation>. Products of the central <primitive idempotents> along restriction paths give its minimal projections. Thus it is a <maximal commutative subalgebra> and a <semisimple algebra>, isomorphic to a finite product of copies of $\mathbb C$.
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