Journal of Operator Theory

Volume 64, Issue 2, Fall 2010 pp. 453-468.

Subfactors and Hadamard matrices

Authors: Remus Nicoara
Author institution: Department of Mathematics, Univ. of Tennessee, 121 Ayres Hall 1403 Circle Dr. Knoxville, TN 37996-1300, U.S.A. and Institute of Mathematics "Simion Stoilow" of the Romanian Academy, 21 Calea Grivitei Street, 010702 - Bucharest, Sector 1, Romania

Summary: To any complex Hadamard matrix $H$ one associates a spin model commuting square, and therefore a hyperfinite subfactor. The standard invariant of this subfactor captures certain "group-like" symmetries of $H$. To gain some insight, we compute the first few relative commutants of such subfactors for Hadamard matrices of small dimensions. Also, we show that subfactors arising from Dita--Haagerup type matrices have intermediate subfactors, and thus their standard invariants have some extra structure besides the Jones projections.

Keywords: Commuting squares, complex Hadamard matrices, subfactors, von Neumann algebras, Jones projection.

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