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Representations of Hecke Algebras at Roots of Unity (Hardcover, 2011)
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Representations of Hecke Algebras at Roots of Unity (Hardcover, 2011)
Series: Algebra and Applications, 15
Expected to ship within 10 - 15 working days
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The 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 the irreducible
representations of Iwahori-Hecke algebras at roots of unity, this
book is a particularly valuable addition to current research in
this field. Using the framework provided by the Kazhdan-Lusztig
theory of cells, the authors develop an analogue of James' (1970)
"characteristic-free'' approach to the representation theory of
Iwahori-Hecke algebras in general. Presenting a systematic and
unified treatment of representations of Hecke algebras at roots of
unity, this book is unique in its approach and includes new results
that have not yet been published in book form. It also serves as
background reading to further active areas of current research such
as the theory of affine Hecke algebras and Cherednik algebras. The
main results of this book are obtained by an interaction of several
branches of mathematics, namely the theory of Fock spaces for
quantum affine Lie algebras and Ariki's theorem, the combinatorics
of crystal bases, the theory of Kazhdan-Lusztig bases and cells,
and computational methods. This book will be of use to researchers
and graduate students in representation theory as well as any
researchers outside of the field with an interest in Hecke
algebras.
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