Introduction by G. de B. Robinson

Summary

In this introduction to the work of James and Kerber I should like to survey briefly the story of developments in the representation theory of the symmetric group. Detailed references will not be possible, but it seems worthwhile to glance at the background which has aroused so much interest in recent years.

The idea of a group goes back a long way and is inherent in the study of the regular polyhedra by the Greeks. It was Galois who systematically developed the connection with algebraic equations, early in the nineteenth century. Not long after, the geometrical relationship between the lines on a general cubic surface and the bitangents of a plane quartic curve aroused the interest of Hesse and Cayley, with a significant contribution by Schläfli in 1858 [1, Chapter IX].* Jordan in his Traité des Substitutions, 1870 [2], and Klein in his Vorlesungen über das Ikosaeder, 1884 [3], added new dimensions to Galois's work. The first edition of Burnside's Theory of Groups of Finite Order appeared in 1897, just at the time when Frobenius's papers in the Berliner Sitzungsberichte were changing the whole algebraic approach. With the appearance of Schur's Thesis [4] in 1901, the need for a revision of Burnside's work became apparent.

Burnside began his preface to the second edition, which appeared in 1911 [5], with the comment: “Very considerable advance in the theory of groups of finite order has been made since the appearance of the first edition of this book.