First order deformations of the Fourier matrix

Journal Article · Wed Jan 15 00:00:00 EST 2014 · Journal of Mathematical Physics

DOI:https://doi.org/10.1063/1.4855476· OSTI ID:22250856

Banica, Teodor ^[1]

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1. Department of Mathematics, Cergy-Pontoise University, 95000 Cergy-Pontoise (France)

The N × N complex Hadamard matrices form a real algebraic manifold C{sub N}. The singularity at a point H ∈ C{sub N} is described by a filtration of cones T{sub H}{sup ×}C{sub N}⊂T{sub H}{sup ∘}C{sub N}⊂T{sub H}C{sub N}⊂T{sup ~}{sub H}C{sub N}, coming from the trivial, affine, smooth, and first order deformations. We study here these cones in the case where H = F{sub N} is the Fourier matrix, (w{sup ij}) with w = e{sup 2πi/N}, our main result being a simple description of T{sup ~}{sub H}C{sub N}. As a consequence, the rationality conjecture dim{sub R}(T{sup ~}{sub H}C{sub N})=dim{sub Q}(T{sup ~}{sub H}C{sub N}∩M{sub N}(Q)) holds at H = F{sub N}.

• OSTI ID: 22250856
• Journal Information: Journal of Mathematical Physics, Vol. 55, Issue 1; Other Information: (c) 2014 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA); ISSN 0022-2488
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
DEFORMATION
FOURIER TRANSFORMATION
MATRICES
SINGULARITY