= Local Artin factors of the standard representation of S3
{c}
{title2=$1/(1-t)^2,\quad1/(1-t^2),\quad1/(1+t+t^2)$}
For the <standard representation of the symmetric group> $S_3$, the unramified <local factor of an Artin L-function>, with $t=p^{-s}$, is respectively the displayed factor for identity, transposition, and three-cycle <Frobenius cycle types>. These follow by removing the trivial summand from the three-point <permutation representation>. If the <inertia group> contains a three-cycle, its invariant subspace in the standard representation is zero, so the ramified local factor is one.
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