Alperin weight conjecture

Statement
Let $$G$$ be a finite group, $$p$$ a prime, and $$B$$ a $$p$$-block (viz an indecomposable summand of the group algebra of $$G$$ over the algebraic closure of $$F_p$$). Then, the following two numbers are equal:


 * The number of irreducible modular characters with block $$B$$
 * The number of $$B$$-weights

Relation with other conjectures
Here is a list of closely related conjectures:


 * Alperin-McKay conjecture
 * Dade invariant conjecture

Symmetric groups and general linear groups
Alperin and Fong, in their paper Weights for symmetric and general linear groups, proved the conjecture for the symmetric groups and for the general linear groups.

Covering groups
Michler and Olsson have verified the conjecture for covering groups of symmetric and alternating groups, in their paper Weights for covering groups of symmetric and alternating groups.