Ja n 20 04 A nested sequence of projectors and corresponding braid matrices R̂ ( θ ) : ( 1 ) Odd dimensions
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چکیده
A nested sequence of projectors and corresponding braid matricesˆR(θ): (1) Odd dimensions. Abstract A basis of N 2 projectors, each an N 2 × N 2 matrix with constant elements, is implemented to construct a class of braid matricesˆR(θ), θ being the spectral parameter. Only odd values of N are considered here. Our ansatz for the projectors P α appearing in the spectral decomposition ofˆR(θ) leads to exponentials exp(m α θ) as the coefficient of P α. The sums and differences of such exponentials on the diagonal and the antidiagonal respectively provide the (2N 2 − 1) nonzero elements ofˆR(θ). One element at the center is normalized to unity. A class of supplementary constraints imposed by the braid equation leaves 1 2 (N + 3)(N − 1) free parameters m α. The diagonalizer ofˆR(θ) is presented for all N. Transfer matrices t(θ) and L(θ) operators corresponding to ourˆR(θ) are studied. Our diagonalizer signals specific combinations of the components of the operators that lead to a quadratic algebra of N 2 constant N × N matrices. The θ-dependence factors out for such combinations. ˆ R(θ) is developed in a power series in θ. The basic difference arising for even dimensions is made explicit. Some special features of ourˆR(θ) are discussed in a concluding section.
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تاریخ انتشار 2004