Titlebook: Representations of Hecke Algebras at Roots of Unity; Meinolf Geck,Nicolas Jacon Book 2011 Springer-Verlag London Limited 2011 Canonical ba

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Specialisations and Decomposition Maps, canonical basic sets for Iwahori-Hecke algebras of classical types. A model case is given by the symmetric group. In another direction, we present a factorisation result for decomposition matrices and present a general formulation of James’ conjecture.

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Hecke Algebras and Finite Groups of Lie Type,rbaki, Iwahori, Tits, which are concerned with the characteristic 0 situation. We then discuss a number of examples and open problems. This includes a conjectural classification of all the irreducible representations of . in the “non-defining characteristic case”.

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,Kazhdan–Lusztig Cells and Cellular Bases,This gives rise to a general theory of “Specht modules” in which Lusztig’s .-function plays, again, a central role. The chapter ends with an elementary treatment of the case where . is the symmetric group.

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1572-5553 ield.Uses a number of concrete examples to clearly explain tThe modular representation theory of Iwahori-Hecke algebras and this theory‘s connection to groups of Lie type is an area of rapidly expanding interest; it is one that has also seen a number of breakthroughs in recent years. In classifying

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Specialisations and Decomposition Maps,unction, we define the key concept of “canonical basic set”. This concept gives a theoritical way to classify the simple modules of Iwahori-Hecke algebras at roots of unity. It is in particular independent of the notion of cellular structure. We develop a general strategy to determine explicitly the

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