Fusion algebras for imprimitive complex reflection groups
Copyright policy )Fusion algebras for imprimitive complex reflection groups
We prove that the Fourier matrices for the imprimitive complex reflection groups introduced by Malle define fusion algebras with not necessarily positive but integer structure constants. Hence they define Z-algebras. As a result, we obtain that all known Fourier matrices belonging to spetses define algebras with integer structure constants.
14 pages
Ordinary representations and characters, Representations of Lie algebras and Lie superalgebras, algebraic theory (weights), Fourier matrices, Algebra and Number Theory, Complex reflection groups, 20F55; 20C33, table algebras, complex reflection groups, Table algebras, Fourier matrix, Reflection and Coxeter groups (group-theoretic aspects), FOS: Mathematics, 20C33, 20F55, Representation theory of finite groups, Representation Theory (math.RT), representations of finite groups, Numerical methods for discrete and fast Fourier transforms, Mathematics - Representation Theory
Ordinary representations and characters, Representations of Lie algebras and Lie superalgebras, algebraic theory (weights), Fourier matrices, Algebra and Number Theory, Complex reflection groups, 20F55; 20C33, table algebras, complex reflection groups, Table algebras, Fourier matrix, Reflection and Coxeter groups (group-theoretic aspects), FOS: Mathematics, 20C33, 20F55, Representation theory of finite groups, Representation Theory (math.RT), representations of finite groups, Numerical methods for discrete and fast Fourier transforms, Mathematics - Representation Theory
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