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 Mar 1 revised A basic question about group representation added 400 characters in body Feb 28 awarded Editor Feb 28 comment A basic question about group representation Sorry, it's a typo. If $\rho$ and $\chi\rho$ are the same irreducible representations, then it contradicts with the fact that every representation is a sum of irreducible ones. Feb 28 revised A basic question about group representation edited body Feb 28 awarded Student Feb 28 asked A basic question about group representation Jan 11 comment Why $\mathbb{C}[T_1, T_2]/(T_2^2 - T_1^3 - 1)$ is isomorphic to $\mathbb{C}[T, \sqrt{T^3+1}]$? Thanks. I will try. Jan 11 comment Why $\mathbb{C}[T_1, T_2]/(T_2^2 - T_1^3 - 1)$ is isomorphic to $\mathbb{C}[T, \sqrt{T^3+1}]$? I see that map, which sends $T_1$ to $T$, $T_2$ to $\sqrt{T^3+1}$. But I don't know how to prove it formally that it is an isomorphism. Jan 11 asked Why $\mathbb{C}[T_1, T_2]/(T_2^2 - T_1^3 - 1)$ is isomorphic to $\mathbb{C}[T, \sqrt{T^3+1}]$?