Charaktertabellen
Charaktertabellen, in English known as character tables, are tabular summaries of the irreducible representations of a finite group. Each table lists the group's conjugacy classes as columns and the irreducible characters as rows. The entry at row χ and column C is the character χ(C) — the trace of any group element in C under the corresponding irreducible representation. The rows encode the representation degrees, while the columns reflect the group's class structure.
Character tables satisfy two key orthogonality relations: row orthogonality and column orthogonality. Concretely, the sum over
Construction typically begins by determining the conjugacy classes, then using the sum-of-squares formula to find possible
Example: for the symmetric group S3 (order 6), there are three irreducible representations: two one-dimensional and
Applications occur in mathematics and physics: character tables classify symmetries, aid in decomposing representations, and provide