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.

Table of Contents

• 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 $w < l$
• 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