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A sophisticated example of this occurs in the theory of monstrous moonshine: the j-invariant is the graded dimension of an infinite-dimensional graded representation of the Monster group, and replacing the dimension with the character gives the McKay–Thompson series for each element of the Monster group.
The characters of irreducible representations are orthogonal. The primary importance of the character group for finite abelian groups is in number theory, where it is used to construct Dirichlet characters. The character group of the cyclic group also appears in the theory of the discrete Fourier transform.
Examples of similar characters in Anglophone culture include Bubbles, Wheeler Walker, Jr. and the stand-up persona of Bob Saget: Grande dame: French for "great lady"; a haughty, flamboyant and elegant woman, prone to extravagant and eccentric fashion. She is usually a stereotype of an elderly high society socialite. [44] [45] [46] [47]
In analytic number theory and related branches of mathematics, a complex-valued arithmetic function: is a Dirichlet character of modulus (where is a positive integer) if for all integers and : [1] χ ( a b ) = χ ( a ) χ ( b ) ; {\displaystyle \chi (ab)=\chi (a)\chi (b);} that is, χ {\displaystyle \chi } is completely multiplicative .
Characterology (from Ancient Greek χαρακτήρ 'character' and ‑λογία, ‑logia) is the academic study of character which was prominent in German-speaking countries during the late 19th and early 20th centuries. [1] [2] It is considered a historic branch of personality psychology, which extended into psychoanalysis and sociology. [3]
Modular representation theory was developed by Richard Brauer from about 1940 onwards to study in greater depth the relationships between the characteristic p representation theory, ordinary character theory and structure of G, especially as the latter relates to the embedding of, and relationships between, its p-subgroups.
The taxonomy is based on a character theory. This character theory consists of four characters: Achievers, Explorers, Socializers, and Killers (often mapped onto the four suits of the standard playing card deck; Diamonds, Spades, Hearts, and Clubs, in that order).
Different characters use different vocabularies and rhythms of speech. For example, some characters are talkative, others taciturn. The way a character speaks can be a powerful way of revealing the character's personality. In theory, a reader should be able to identify which character is speaking simply from the way they talk. [11]