decomposeCharacter(c,T)
c/T
This function is provided by the package BettiCharacters.
Use the decomposeCharacter method to decompose a character into a linear combination of irreducible characters in a character table. The shortcut c/T is equivalent to the command decomposeCharacter(c,T).
As an example, we construct the character table of the symmetric group on 3 elements, then use it to decompose the character of the action of the same symmetric group permuting the variables of a standard graded polynomial ring.









The results are shown in a table whose rows are indexed by pairs of homological and internal degrees, and whose columns are labeled by the irreducible characters. By default, irreducible characters in a character table are labeled as X0, X1, ..., etc, and the same labeling is inherited by the character decompsoition. The user may pass custom labels in a list using the option Labels when constructing the character table.
The object decomposeCharacter is a method function.