Abstract
In this chapter, we study non semisimple Iwahori-Hecke algebras in the spirit of Brauer’s classical modular representation theory. Using Lusztig’s a-function, 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 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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© 2011 Springer-Verlag London Limited
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Geck, M., Jacon, N. (2011). Specialisations and Decomposition Maps. In: Representations of Hecke Algebras at Roots of Unity. Algebra and Applications, vol 15. Springer, London. https://doi.org/10.1007/978-0-85729-716-7_3
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DOI: https://doi.org/10.1007/978-0-85729-716-7_3
Publisher Name: Springer, London
Print ISBN: 978-0-85729-715-0
Online ISBN: 978-0-85729-716-7
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