Let $S_n$ be the symmetric group on the set $\{1,2,\ldots,n\}$ and $K$ a field of characterize $0$.
The definition of cellular algebra refers to https://en.wikipedia.org/wiki/Cellular_algebra . I have known that the group algebra $KS_n$ is a cellular algebra. But I cannot give cellular bases of $KS_n$. Who can give cellular bases of $KS_n$? Any help is needed.