Weight for a finite group
Definition with symbols
let be a prime and a finite group. A weight of is a pair such that:
- is a -subgroup of , and in fact, (viz it is the -Sylow core of its normalizer ).
- is an irreducible character of , the restriction of to is trivial, and belongs to a -block of of defect zero.
Two weights are said to be equal if their is an inner automorphism of taking one to the other.
Weights for a block
For a -block of , the weight is said to eb a -weight if where is the associated block on .