The dimension of representation refers to the size of a vector space associated with a representation of a group or algebra, specifically indicating how many basis vectors are needed to describe the action of the group on a vector space. This concept is crucial in understanding how groups can act on spaces, leading to insights in both harmonic analysis and the study of specific groups like SU(2) and SO(3). A higher dimension suggests a more complex representation, which can impact the way functions or signals behave under group actions.
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