By Andrew Mathas
This quantity provides an absolutely self-contained advent to the modular illustration concept of the Iwahori-Hecke algebras of the symmetric teams and of the $q$-Schur algebras. The research of those algebras was once pioneered by way of Dipper and James in a sequence of landmark papers. the first objective of the e-book is to categorise the blocks and the straightforward modules of either algebras. the ultimate bankruptcy includes a survey of modern advances and open difficulties. the most effects are proved by way of exhibiting that the Iwahori-Hecke algebras and $q$-Schur algebras are mobile algebras (in the feel of Graham and Lehrer). this can be proved by way of showing traditional bases of either algebras that are listed via pairs of ordinary and semistandard tableaux respectively. utilizing the equipment of mobile algebras, that's built in bankruptcy 2, this leads to a fresh and stylish class of the irreducible representations of either algebras. The block concept is approached by way of first proving an analogue of the Jantzen sum formulation for the $q$-Schur algebras. This publication is the 1st of its variety masking the subject. It deals a considerably simplified therapy of the unique proofs. The ebook is an effective reference resource for specialists. it is going to additionally function an exceptional creation to scholars and starting researchers for the reason that each one bankruptcy comprises routines and there's an appendix containing a short improvement of the illustration thought of algebras. A moment appendix offers tables of decomposition numbers.
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