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Blocks with defect group [math]C_3[/math]

These are blocks with cyclic defect groups and so they are described by Brauer trees.

There are two [math]\mathcal{O}[/math]-Morita equivalence classes, accounting for all the possible Brauer trees.

Class Representative # lifts / [math]\mathcal{O}[/math] [math]k(B)[/math] [math]l(B)[/math] Inertial quotients [math]{\rm Pic}_\mathcal{O}(B)[/math] [math]{\rm Pic}_k(B)[/math] [math]{\rm mf_\mathcal{O}(B)}[/math] [math]{\rm mf_k(B)}[/math] Notes
M(3,1,1) [math]kC_3[/math] 1 3 1 [math]1[/math] [math]S_3[/math] [math]k:k^*[/math] 1 1 M(3,1,1)tree.png
M(3,1,2) [math]kS_3[/math] 1 3 2 [math]C_2[/math] [math]C_2[/math] [math]k^* \times C_2[/math] 1 1 M(3,1,2)tree.png