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The multivariate Krawtchouk polynomials as matrix elements of the rotation group representations on oscillator states

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arxiv 1306.4256 v3 pith:4DYFSMZZ submitted 2013-06-18 math-ph math.MP

classification math-phmath.MP
keywords polynomialskrawtchoukelementsmatrixrepresentationsalgebraicbivariatedimensions
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An algebraic interpretation of the bivariate Krawtchouk polynomials is provided in the framework of the 3-dimensional isotropic harmonic oscillator model. These polynomials in two discrete variables are shown to arise as matrix elements of unitary reducible representations of the rotation group in 3 dimensions. Many of their properties are derived by exploiting the group-theoretic setting. The bivariate Tratnik polynomials of Krawtchouk type are seen to be special cases of the general polynomials that correspond to particular rotations involving only two parameters. It is explained how the approach generalizes naturally to (d+1) dimensions and allows to interpret multivariate Krawtchouk polynomials as matrix elements of SO(d+1) unitary representations. Indications are given on the connection with other algebraic models for these polynomials.

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Cited by 2 Pith papers

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  1. The quantum loop algebra of $sl_2$ and $q$-Racah type bivariate functions

    math.QA 2026-07 conditional novelty 6.0 of 10

    Bivariate q-Racah-type functions are realized as overlaps of six distinguished eigenbases in tensor-product evaluation representations of L U_q sl2, one family linked to tridiagonal pairs and another conjecturally to ...

  2. Exactly solvable multicomponent spinless fermions

    hep-th 2025-02 conditional novelty 5.0 of 10

    Four exactly solvable multicomponent spinless fermion models are constructed from multivariate Krawtchouk, Meixner, and two Rahman-like polynomial families.

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