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Results tagged with modular-representation-theory
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user 35416
For questions about modular representation theory, the study of representations over a field of positive characteristic.
7
votes
Accepted
Defect groups and subgroups
This is an exercise in writing out the definitions:
since the defect group of $B$ is $E$, we have $B|(B_{\delta(E)})^{G\times G}$. So by assumption,
$$
b\;|\;B_{H\times H}\;|\;\left((B_{\delta(E)})^{G …
- 13k
6
votes
Accepted
Irreducible mod-p representation of a semidirect product with trivial p-core
The following is a direct proof that any extension of $G$ by $V$ splits. It is taken from a joint paper of mine with Tim Dokchitser, where the proof starts in the last paragraph of page 12.
First, no …
- 13k
1
vote
Reference for fact about reduction mod $p$ of a representation of a finite group
I don't know of just a citation, but here is a pretty quick way to deduce this from the literature (I imagine that this might be the argument you had in mind, in which case apologies for telling you t …
- 13k