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character (Definition)

Let $\rho: G \longrightarrow \operatorname{GL}(V)$ be a finite dimensional representation of a group $G$ (i.e., $V$ is a finite dimensional vector space over its scalar field $K$ . The character of $\rho$ is the function $\chi_V: G \longrightarrow K$ defined by $$ \chi_V(g) := \operatorname{Tr}(\rho(g)) $$ where $\operatorname{Tr}$ is the trace function.

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Cross-references: inner product, orthonormal, multiplication, pointwise addition, basis, complex numbers, irreducible, finite, class function, conjugate, properties, trace, function, field, scalar, vector space, group, representation, finite dimensional
There are 16 references to this entry.

This is version 4 of character, born on 2002-02-07, modified 2003-02-10.
Object id is 1843, canonical name is Character.
Accessed 11565 times total.

Classification:
AMS MSC20C99 (Group theory and generalizations :: Representation theory of groups :: Miscellaneous)

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