Abstract
We develop a method of construction of transformation matrix between two bases of the model of Heisenberg magnet. The first one is a natural basis of magnetic configurations while the second is adjusted to the irreducible basis of the duality of Weyl. Proposed method allows us to calculate each matrix element separately, so it does not depend on the dimension of the system. Calculation of a matrix elements is given by ladder construction of consecutive letters of magnetic configurations along the well known Robinson-Schensted algorithm. In this way we obtain a graph with vertices given by Gelfand patterns and edges labelled by insertion algorithm. This graph allows us to read off all Clebsch-Gordan coefficients for a unitary group U(n) and then to calculate the matrix element.
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