The blocks and weights of finite special linear and unitary groups.

Abstract This paper has two main parts. First, we give a classification of the ℓ -blocks of finite special linear and unitary groups SL n (ϵ q) in the non-defining characteristic ℓ ≥ 3. Second, we describe how the ℓ -weights of SL n (ϵ q) can be obtained from the ℓ -weights of GL n (ϵ q) when ℓ ∤ gcd (n , q − ϵ) , and verify the Alperin weight conjecture for SL n (ϵ q) under the condition ℓ ∤ gcd (n , q − ϵ). As a step to establish the Alperin weight conjecture for all finite groups, we prove the inductive blockwise Alperin weight condition for any unipotent ℓ -block of SL n (ϵ q) if ℓ ∤ gcd (n , q − ϵ). [ABSTRACT FROM AUTHOR]