Regular Representation of G

Let g be the order of G, and let V be a vector space of dimension g, with a basis (e_t)_{t\in G} indexed by the elements t of G. For s\in G, let \rho_s be the linear map of V into V which sends e_t to e_{st}; this defines a linear representation, which is called the regular representation of G.

Source: Linear Representations of Finite Groups (Graduate Texts in Mathematics) (v. 42)

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