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Group Representation Restriction

A group representation of a group G on a vector space V can be restricted to a subgroup H. For example, the symmetric group on three letters has a representation phi on R^2 by

phi(e)=[ 1 0; 0 1]
(1)
phi(12)=[ 0 1; 1 0]
(2)
phi(13)=[ -1 0; -1 1]
(3)
phi(23)=[ 1 -1; 0 -1]
(4)
phi(123)=[ -1 1; -1 0]
(5)
phi(132)=[ 0 -1; 1 -1]
(6)

that can be restricted to the subgroup of group order 3,

phi(e)=[ 1 0; 0 1]
(7)
phi(123)=[ -1 1; -1 0]
(8)
phi(132)=[ 0 -1; 1 -1].
(9)

See also

Group Representation, Vector Space

This entry contributed by Todd Rowland

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Cite this as:

Rowland, Todd. "Group Representation Restriction." From MathWorld--A Wolfram Resource, created by Eric W. Weisstein. https://mathworld.wolfram.com/GroupRepresentationRestriction.html

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