High Quality Content by WIKIPEDIA articles! In mathematics, and in particular the theory of group representations, the regular representation of a group G is the linear representation afforded by the group action of G on itself. One distinguishes the left regular representation ? induced by the multiplication with the inverse on the left and the right regular representation ?, which comes from the multiplication on the right. In formulas, it is To say that G acts on itself by multiplication is tautological. If we consider this action as a permutation representation it is characterised as having a single orbit and stabilizer the identity subgroup {e} of G. The regular representation of G, for a given field K, is the linear representation made by taking the permutation representation as a set of basis vectors of a vector space over K.

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