Abstract
FELIX KLEIN'S famous enunciation—“Given a manifold and a group of transformations of the same, to develop the theory of invariants relating to that group”—not only describes the spirit of geometry but also reveals that the concept of a group dominated at least one important branch of mathematics. In the fundamental structure of other branches, however, groups are to be found, and the general concepts developed during the latter half of the last century both by Klein and his student friend, Sophus Lie, were responsible for the far-reaching influence which the relevant theory has had on modern mathematical thought. It is not always easy to discover the first important application of a newly developed theory but it is probable that the formulation of the mechanics of the atom made by Heisenberg in 1926 by the application of the theory of matrices—the invention of Cayley in 1858—is a fair illustration of the excursion of that theory into the practical domain.
The Theory of Group Representations
By Prof. Francis D. Murnaghan. Pp. xi + 369. (Baltimore, Md.: Johns Hopkins Press; London: Oxford University Press, 1938.) 22s. 6d. net.
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BROWN, F. The Theory of Group Representations. Nature 146, 283 (1940). https://doi.org/10.1038/146283a0
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DOI: https://doi.org/10.1038/146283a0
