C25
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Blocks with defect group [math]C_{25}[/math]
These are blocks with cyclic defect groups and so they are described by Brauer trees.
There are 12 possible Brauer trees. It is not known which give rise to [math]\mathcal{O}[/math]-Morita equivalence classes.
CLASSIFICATION INCOMPLETE
| Class | Representative | [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 |
|---|---|---|---|---|---|---|---|---|---|
| [math]M(25,1,1)[/math] | [math]kC_{25}[/math] | 25 | 1 | [math]1[/math] | [math]C_{25} : C_{20}[/math] | 1 | 1 | ||
| [math]M(25,1,2)[/math] | [math]kD_{50}[/math] | 14 | 2 | [math]C_2[/math] | 1 | 1 | |||
| [math]M(25,1,3)[/math] | [math]B_0(kPSL_2(49))[/math] | 14 | 2 | [math]C_2[/math] | 1 | 1 | |||
| [math]M(25,1,4)[/math] | [math]k(C_{25}:C_4)[/math] | 10 | 4 | [math]C_4[/math] | [math]C_4[/math] | 1 | 1 | ||
| [math]M(25,1,5)[/math] | [math]B_0(kSz(32))[/math] | 10 | 4 | [math]C_4[/math] | 1 | 1 |
Blocks in [math]M(25,1,2)[/math] are derived equivalent (over [math]\mathcal{O}[/math]) to those in [math]M(25,1,3)[/math].
Blocks in [math]M(25,1,4)[/math] are derived equivalent (over [math]\mathcal{O}[/math]) to those in [math]M(25,1,5)[/math].
