Orthogonality of the Hi-Jack Polynomials Associated with the Calogero Model.

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  • Ujino Hideaki
    Department of Physics, Graduate School of Science, The University of Tokyo, Hongo 7–3–1, Bunkyo–ku, Tokyo 113
  • Wadati Miki
    Department of Physics, Graduate School of Science, The University of Tokyo, Hongo 7–3–1, Bunkyo–ku, Tokyo 113

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  • Orthogonality of the Hi-Jack Polynomial

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Orthogonality of the Hi-Jack polynomials, which were introduced asthe simultaneous eigenfunctions of the first and second conserved operatorsof the Calogero model, is proved by showing that they are non-degeneratesimultaneous eigenfunctions for all the commuting conserved operators ofthe Calogero model.The fact that our definition of the Hi-Jack polynomials uniquely specifiesthe Hi-Jack polynomials, which is assured by the triangularity withrespect to the dominance order among the Young tableaux, plays an essential role in our proof.

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