Texts and Readings in Mathematics

This book serves several purposes. The first and foremost is to give an elementary introduction to the basic concepts of the theory of ordinary representations to finite groups with a minimum of prerequisites.

The second purpose, which is also the main theme of this exposition, is to be able to do the theory rather explicitly for the important special case of the symmetric groups Sn of permutations on n letters.

The third purpose is to use the preparatory material of the first two parts, coupled with the Sn theory, to do the same for some other important special groups, namely, the alternating group An and the hyperoctahedral groups Bn and Dn.
Part I : The Structure of Semi-simple Rings.
1. Preliminaries.
2. Semi-simple Rings and Brauer Group.

Part II. Representations of Finite Groups.
3. Representations of Finite Groups.
4. Induced Representations.

Part III. Representations of the Symmetric and Alternating Groups.
5. Representations of the Symmetric Group Sn
6. Representations of the Alternating group An.

Part IV. Representations of the Hyperoctahedral Groups Bn and Dn
7. Representations of the Hyperoctahedral Group Bn
8. Representations of the Hyperoctahedral Group Dn.