Example
For the special linear group SLn, the unipotent conjugacy classes are parametrized by partitions of n: if u is a unipotent element, the corresponding partition is given by the sizes of the Jordan blocks of u. All groups A(u) are trivial.
The Weyl group W is the symmetric group Sn on n letters. Its irreducible representations over a field of characteristic zero are also parametrized by the partitions of n. The Springer correspondence in this case is a bijection, and in the standard parametrizations, it is given by transposition of the partitions (so that the trivial representation of the Weyl group corresponds to the regular unipotent class, and the sign representation corresponds to the identity element of G).
Read more about this topic: Springer Correspondence
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