  A coplactic class in the symmetric group S_n consists of all permutations in
S_n with a given Schensted Q-symbol, and may be described in terms of local
relations introduced by Knuth. Any Lie element in the group algebra of S_n
which is constant on coplactic classes is already constant on descent classes.
As a consequence, the intersection of the Lie convolution algebra introduced by
Patras and Reutenauer and the coplactic algebra introduced by Poirier and
Reutenauer is the Solomon descent algebra.
