= Decomposition matrix
{disambiguate=modular representation theory}
{title2=$D$}
The decomposition <matrix> is a specific invariant of <modular representation theory>.
The decomposition <matrix> records the multiplicities of simple modular representations in reductions of ordinary representations. If its rows are indexed by ordinary irreducible characters and its columns by irreducible Brauer characters, its entry $d_{\chi\phi}$ is the decomposition number of $\phi$ in the reduction of $\chi$.
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