Character tables of Weyl groups in GAP.

*(English)*Zbl 0830.20023The character tables of symmetric groups were already known to Frobenius. Meanwhile many people have contributed to the representation theory of symmetric groups and related topics. A self contained overview of the theory is given in the book The representation theory of the symmetric group (1981; Zbl 0491.20010) by G. D. James and A. Kerber. We will use this book as a guideline for an implementation of the character tables of the series of Weyl groups of type \(A\), \(B\), and \(D\) and some related groups. We will also prove two theorems about character values of wreath products with symmetric groups (see 4.4) and Weyl groups of type \(D\) (see 5.1). For the exceptional Weyl groups of type \(G_2\), \(F_4\), \(E_6\), \(E_7\) or \(E_8\) we will identify the characters as they are stored in the GAP library with their labels in R. W. Carter’s book Finite groups of Lie type: Conjugacy classes and complex characters (1985; Zbl 0567.20023).

##### MSC:

20C30 | Representations of finite symmetric groups |

20C40 | Computational methods (representations of groups) (MSC2010) |