The Lie Module Function for Symmetric Groups^#

^#Communicated by B. Parshall.

Let V be a ℂ G-module where ℂ is the field of all complex numbers and G is a symmetric group. The purpose of this article is to give a method of analyzing the Lie powers L ⁿ (V ), for every positive integer n, by making use of the recent work of Bryant.

Key Words:

• Free Lie algebra
• Formal power series
• Green algebra
• Symmetric group

Mathematics Subject Classification:

• Primary 17B01
• Secondary 20C30

ACKNOWLEDGMENT

I would like to thank Professor R. M. Bryant for his support and encouragement during the writing of this article.

Notes

^#Communicated by B. Parshall.