Kostka matrices at the level of bases and the complete set of commuting Jucys-Murphy operators |
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Authors: | B Lulek P Jakubczyk |
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Institution: | a The Faculty of Mathematics and Applied Physics, Rzeszow University of Technology, W. Pola 2, 35-059 Rzeszów, Poland b Institute of Physics, University of Rzeszów, ul. Rejtana 16c, 35-959 Rzeszów, Poland |
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Abstract: | A method for evaluation of Kostka matrices at the level of bases, and determination of related irreducible basis of the Weyl duality is proposed. The method bases on Jucys-Murphy operators which constitute a complete set of commuting Hermitian operators along the general Dirac formalism of quantum mechanics, applied to the algebra of a symmetric group. The way of construction of appropriate projection operators is pointed out, and the combinatorial meaning of the path on the Young graph, corresponding to a standard Young tableau, is made transparent. |
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Keywords: | 02 20 &minus a 03 67 Lx 03 67 Mn 71 10 Li 75 10 Pq |
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