"Twisted" Dimension
One may interpret the character of a representation as the "twisted" dimension of a vector space. Treating the character as a function of the elements of the group χ(g), its value at the identity is the dimension of the space, since Accordingly, one can view the other values of the character as "twisted" dimensions.
One can find analogs or generalizations of statements about dimensions to statements about characters or representations. 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.
Read more about this topic: Character Theory
Famous quotes containing the words twisted and/or dimension:
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