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Number Theory --- Forms (Mathematics) --- Cyclotomy

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This monograph contributes to the existence theory of difference sets, cyclic irreducible codes and similar objects. The new method of field descent for cyclotomic integers of presribed absolute value is developed. Applications include the first substantial progress towards the Circulant Hadamard Matrix Conjecture and Ryser`s conjecture since decades. It is shown that there is no Barker sequence of length l with 13<1<4x10^(12). Finally, a conjecturally complete classification of all irreducible cyclic two-weight codes is obtained.

Cyclotomy. --- Difference sets. --- Finite geometries. --- Difference sets --- Cyclotomy --- Finite geometries --- Algebra --- Mathematical Theory --- Mathematics --- Physical Sciences & Mathematics --- Combinatorics. --- Combinatorics --- Mathematical analysis

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Discrete mathematics --- Number theory --- Algebraic fields. --- Combinatorial designs and configurations. --- Cyclotomy. --- Algèbre --- Analyse combinatoire --- Algèbre --- Block design

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511.6 --- Algebraic number fields --- Algebraic fields. --- Cyclotomy. --- 511.6 Algebraic number fields --- Nombres, Théorie des

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The definition of Rouquier for the families of characters introduced by Lusztig for Weyl groups in terms of blocks of the Hecke algebras has made possible the generalization of this notion to the case of complex reflection groups. The aim of this book is to study the blocks and to determine the families of characters for all cyclotomic Hecke algebras associated to complex reflection groups. This volume offers a thorough study of symmetric algebras, covering topics such as block theory, representation theory and Clifford theory, and can also serve as an introduction to the Hecke algebras of complex reflection groups.

Hecke algebras --- Representations of groups --- Cyclotomy --- Mathematics --- Physical Sciences & Mathematics --- Mathematical Theory --- Algebra --- Cyclotomy. --- Hecke algebras. --- Representations of groups. --- Group representation (Mathematics) --- Groups, Representation theory of --- Algebras, Hecke --- Equations, Cyclotomic --- Mathematics. --- Group theory. --- Group Theory and Generalizations. --- Groups, Theory of --- Substitutions (Mathematics) --- Math --- Science --- Group algebras --- Number theory --- Equations, Abelian --- Group theory