J. Aust. Math. Soc.  75 (2003), 9-21
Multiplicities of higher Lie characters

Manfred Schocker
  Mathematical Institute
  24--29 St Giles
  Oxford OX1 3LB

The higher Lie characters of the symmetric group $S_n$ arise from the Poincaré-Birkhoff-Witt basis of the free associative algebra. They are indexed by the partitions of $n$ and sum up to the regular character of $S_n$. A combinatorial description of the multiplicities of their irreducible components is given. As a special case the Kraskiewicz-Weyman result on the multiplicities of the classical Lie character is obtained.
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