1. Second order deformations of group commuting squares and Hadamard matrices.
- Author
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Nicoara, Remus and White, Joseph
- Subjects
HADAMARD matrices ,COMPLEX matrices ,ABELIAN groups ,FINITE groups ,SQUARE ,DEFORMATION of surfaces - Abstract
In [Indiana Univ. Math. J. 60 (2011), pp. 847-857] the first author introduced second order necessary conditions for a commuting square to admit sequential deformations in the moduli space of non-isomorphic commuting squares. In this paper we investigate these conditions for commuting squares C
G constructed from finite groups G. We are especially interested in the case G = Zn , since deformations of CZn correspond to deformations of the Fourier matrix Fn in the moduli space of non-equivalent complex Hadamard matrices. We show that for G = Zn the second order conditions follow automatically from the first order conditions, but this is not necessarily true for other finite abelian groups G. Our result gives a complete description of the second order deformations of the Fourier matrix Fn in the moduli space of non-equivalent complex Hadamard matrices. [ABSTRACT FROM AUTHOR]- Published
- 2020
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