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Second order deformations of group commuting squares and Hadamard matrices.
- Source :
-
Proceedings of the American Mathematical Society . Sep2020, Vol. 148 Issue 9, p3967-3974. 8p. - Publication Year :
- 2020
-
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 CG 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]
Details
- Language :
- English
- ISSN :
- 00029939
- Volume :
- 148
- Issue :
- 9
- Database :
- Academic Search Index
- Journal :
- Proceedings of the American Mathematical Society
- Publication Type :
- Academic Journal
- Accession number :
- 144503632
- Full Text :
- https://doi.org/10.1090/proc/15025