Gelfand–Tsetlin basis
= Gelfand–Tsetlin basis
{c}
Successively decompose an <irreducible representation> along a subgroup chain with <multiplicity-free restriction>. A complete path selects a one-dimensional subspace; choosing one nonzero vector on each path gives a Gelfand–Tsetlin basis. For a <symmetric group> over the <complex numbers>, paths are <standard Young tableaux>, and the <Young–Jucys–Murphy elements> act diagonally with their cell contents.