= Jucys–Murphy description of the center of a symmetric-group algebra
{c}
{title2=$Z(FS_n)=\{f(J_1,\ldots,J_n):f\text{ symmetric}\}$}
The <Young–Jucys–Murphy elements> commute, and <symmetric polynomials> in them are central. The full center theorem holds integrally as well as over <fields>, so it survives modular reduction. On an ordinary <Specht module>, the scalar of such a <polynomial> is its value on the cell-content multiset. The integral generation step is stronger than knowing this description only over a characteristic-zero <field> and is essential in the modular block argument.
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