Difference between revisions of "C25"
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(Switched M(25,1,5) and M(25,1,6) to match C5 labellings) |
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|[[M(25,1,1)]] || <math>kC_{25}</math> ||25 ||1 || <math>1</math> ||<math>C_{25} : C_{20}</math> || ||1 ||1 || | |[[M(25,1,1)]] || <math>kC_{25}</math> ||25 ||1 || <math>1</math> ||<math>C_{25} : C_{20}</math> || ||1 ||1 || | ||
|- | |- | ||
| − | |[[M(25,1,2)]] || <math>kD_{50}</math> ||14 ||2 || <math>C_2</math> || || ||1 ||1 || | + | |[[M(25,1,2)]] || <math>kD_{50}</math> ||14 ||2 || <math>C_2</math> || <math>C_2 \times C_{10}</math> || ||1 ||1 || |
|- | |- | ||
| − | |[[M(25,1,3)]] || <math>B_0(kPSL_2(49))</math> ||14 ||2 || <math>C_2</math> || || ||1 ||1 || | + | |[[M(25,1,3)]] || <math>B_0(kPSL_2(49))</math> ||14 ||2 || <math>C_2</math> || <math>C_{10}</math> || ||1 ||1 || |
|- | |- | ||
| − | |[[M(25,1,4)]] || <math>k(C_{25}:C_4)</math> ||10 ||4 || <math>C_4</math> || <math>C_4</math> || ||1 ||1 || | + | |[[M(25,1,4)]] || <math>k(C_{25}:C_4)</math> ||10 ||4 || <math>C_4</math> || <math>C_4 \times C_5</math> || ||1 ||1 || |
|- | |- | ||
| − | |[[M(25,1,5)]] || <math>B_0( | + | |[[M(25,1,5)]] || <math>B_0(kPGL_2(49))</math> ||10 ||4 || <math>C_4</math> || <math>C_5</math> || ||1 ||1 || |
|- | |- | ||
| − | |[[M(25,1,6)]] || <math>B_0( | + | |[[M(25,1,6)]] || <math>B_0(kSz(32))</math> ||10 ||4 || <math>C_4</math> || <math>C_5</math> || ||1 ||1 || |
|} | |} | ||
Revision as of 07:14, 28 September 2018
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 |
|---|---|---|---|---|---|---|---|---|---|
| M(25,1,1) | [math]kC_{25}[/math] | 25 | 1 | [math]1[/math] | [math]C_{25} : C_{20}[/math] | 1 | 1 | ||
| M(25,1,2) | [math]kD_{50}[/math] | 14 | 2 | [math]C_2[/math] | [math]C_2 \times C_{10}[/math] | 1 | 1 | ||
| M(25,1,3) | [math]B_0(kPSL_2(49))[/math] | 14 | 2 | [math]C_2[/math] | [math]C_{10}[/math] | 1 | 1 | ||
| M(25,1,4) | [math]k(C_{25}:C_4)[/math] | 10 | 4 | [math]C_4[/math] | [math]C_4 \times C_5[/math] | 1 | 1 | ||
| M(25,1,5) | [math]B_0(kPGL_2(49))[/math] | 10 | 4 | [math]C_4[/math] | [math]C_5[/math] | 1 | 1 | ||
| M(25,1,6) | [math]B_0(kSz(32))[/math] | 10 | 4 | [math]C_4[/math] | [math]C_5[/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].
