In
mathematics, an induced character is the
character
Character or Characters may refer to:
Arts, entertainment, and media Literature
* ''Character'' (novel), a 1936 Dutch novel by Ferdinand Bordewijk
* ''Characters'' (Theophrastus), a classical Greek set of character sketches attributed to The ...
of the
representation
Representation may refer to:
Law and politics
*Representation (politics), political activities undertaken by elected representatives, as well as other theories
** Representative democracy, type of democracy in which elected officials represent a ...
''V'' of a
finite group ''G''
induced
Induce may refer to:
* Induced consumption
* Induced innovation
* Induced character
* Induced coma
* Induced menopause
* Induced metric
* Induced path
* Induced topology
* Induce (musician), American musician
See also
* Inducement (disambiguation ...
from a representation ''W'' of a
subgroup
In group theory, a branch of mathematics, given a group ''G'' under a binary operation ∗, a subset ''H'' of ''G'' is called a subgroup of ''G'' if ''H'' also forms a group under the operation ∗. More precisely, ''H'' is a subgrou ...
''H'' ≤ ''G''. More generally, there is also a notion of
induction of a
class function
In mathematics, especially in the fields of group theory and representation theory of groups, a class function is a function on a group ''G'' that is constant on the conjugacy classes of ''G''. In other words, it is invariant under the conjug ...
''f'' on ''H'' given by the formula
:
If ''f'' is a character of the representation ''W'' of ''H'', then this formula for
calculates the character of the induced representation ''V'' of ''G''.
[. Translated from the second French edition by Leonard L. Scott.]
The basic result on induced characters is
Brauer's theorem on induced characters. It states that every irreducible character on ''G'' is a
linear combination with integer coefficients of characters induced from
elementary subgroups.
References
Group theory
{{algebra-stub