Consider representation theory associated to symmetric groups, or to Hecke algebras in type A, or to $q$-Schur algebras, or to finite general linear groups in non-describing characteristic. Rock blocks are certain combinatorially defined blocks appearing in such a representation theory, first observed by R. Rouquier. Rock blocks are much more symmetric than general blocks, and every block is derived equivalent to a Rock block. Motivated by a theorem of J. Chuang and R. Kessar in the case of symmetric group blocks of abelian defect, the author pursues a structure theorem for these blocks.
Introduction; Highest weight categories, $q$-Schur algebras, Hecke algebras, and finite general linear groups; Blocks of $q$-Schur algebras, Hecke algebras, and finite general linear groups; Rock blocks of finite general linear groups and Hecke algebras, when $w <|$; Rock blocks of symmetric groups, and the Brauer morphism; Schur-Weyl duality inside Rock blocks of symmetric groups; Ringel duality inside Rock blocks of symmetric groups; James adjustment algebras for Rock blocks of symmetric groups; Doubles, Schur super-bialgebras, and Rock blocks of Hecke algebras; Power sums; Schiver doubles of type $A \infty$; Bibliography; Index.