The inductive blockwise Alperin weight condition for type $\mathsf C$ and the prime $2$

Abstract

We establish the inductive blockwise Alperin weight condition for simple groups of Lie type C and the bad prime 2. As a main step, we derive a labelling set for the irreducible 2-Brauer characters of the finite symplectic groups Sp 2n (q) (with odd q), together with the action of automorphisms. As a further important ingredient we prove a Jordan decomposition for weights.

On the inductive blockwise Alperin weight condition for the unipotent blocks of finite groups of Lie type E_6

“…Du), pcli17@pku.edu.cn (P. Li), zsy0509@pku.edu.cn (S. Zhao). groups, simple groups of type 2 F 4 , see [37]; simple groups of Lie type in the defining characteristic, simple groups of type 2 B 2 and 2 G 2 , see [41]; simple groups of type G 2 and 3 D 4 , see [40]; some cases of type A, see [16], [17] and [19]; the case of type C under the assumption that the decomposition matrix with respect to E(G, l ′ ) is unitriangular, see [20] and [29]; unipotent blocks of classical groups, see [18].…”

A criterion for the inductive Alperin weight condition

“…During the preparation of this note various authors used our criterion already verifying the inductive Alperin weight condition and the inductive blockwise Alperin weight condition for families of simple groups of Lie type, see [FLZ20a,Li20,FLZ20b,FM20].…”

Equivariant correspondences and the inductive Alperin weight condition for type $\mathsf A$

“…The inductive (BAW) condition has been verified for several families of simple groups so far: groups of Lie type in their defining characteristic (Späth [56]); simple alternating groups, Suzuki groups and Ree groups (Malle [46]); many of the 26 sporadic groups ( [10]); blocks with cyclic defect groups (Koshitani-Späth [38,39]); groups of Lie type G 2 and 3 D 4 (Schulte [54]); a special case of type A (C. Li-Zhang [43,44]); unipotent blocks of type A (Feng [23]); blocks of type A with abelian defect (Brough-Späth [14]); certain cases of classical groups (Feng-Z. Li-Zhang [26]); groups of type C (C. Li [40,41], Feng-Malle [27]); some more particular simple classical groups of small rank ( [12,21,22,24,42,53]). We mention that the inductive (AW) condition holds for all of the above cases since the inductive (BAW) condition implies the inductive (AW) condition.…”