# Questions tagged [characters]

For questions about characters (traces of representations of a group on a vector space).

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### An identity about the sum of the reciprocal of the irreducible character of a symmetric group evauated at identity

I just learnt character theory and I am reading the paper https://academic.oup.com/jlms/article-abstract/66/3/623/811347 which is a quite beautiful paper. Section 4.3, on p. 631 contains an inequality ...
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### Orthogonality and completeness of irreducible representations

I am reading a paper https://arxiv.org/abs/1910.07143 I am unable to understand the construction of table III, for the section Orthogonality and completeness of matrix elements in group space. The ...
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### Character table of S4

I am trying to understand the character table of $S_4$. I have obtained the trivial, signature and standard representations. The fourth one is the product of signature and standard. Now for the last ...
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### Constructing the character table of Octahedral Group (order 48)

I am trying to construct the character table for the symmetry group of Cube, $O_h$, which as 48 elements. I figured out that there are 10 classes. Now, as a consequence of the great orthogonality ...
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### Determining which characters split or fuse

The ATLAS seems to suppose that in the case $G.2$ it is easy to determine which irreducible characters of $G$ will split and which will fuse in the extension. Is there is a source which can explain ...
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### How to read labels of character tables in SageMath (and GAP)?

Note: SageMath's Group.character_table() method is built as a wrapper for GAP's CharacterTable() function. Let $G = \text{Sym}_4$...
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### The character table of $G/Z(G)$ and $G/N$ given knowledge of the character table of $G$
Suppose for a group $G$, of which we completely understand its conjugacy class structure and character table, is there a simple algorithm to deduce the character table of $G/Z(G)$? Or more generally, \$...