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A Special Formula for the Lie Character

Published online by Cambridge University Press:  20 November 2018

Robert L. Davis
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In 1942 Thrall (3) introduced what he called the Lie character to study the structure of the free Lie ring. These characters are defined by associative representations of the full linear group GLq(C). Their importance is seen in the fact that, for each n, the splitting of the submodule of Lie forms of degree n into irreducible invariant subspaces is completely specified by the Lie character ζn.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 10 , 1958 , pp. 33 - 38
Copyright
Copyright © Canadian Mathematical Society 1958

References

1. Brandt, A., The free Lie ring and Lie representations of the full linear group, Trans. Amer. Math. Soc, 56 (1944), 528-536.Google Scholar
2. Murnaghan, F. D., The Theory of Group Representations (Baltimore, 1938).Google Scholar
3. Thrall, R. M., On symmetrized Kronecker powers and the structure of the free Lie ring, Amer. J. Math., 64 (1942), 371-388.Google Scholar
4. Weyl, Hermann, The Classical Groups (Princeton, 1946).Google Scholar
5. Witt, E., Treue Darstellung Liescher Ringe, J. reine angew. Math., 177 (1937), 152-160.Google Scholar