Перегляд за автором "Dunkl, C.F."

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  • A Linear System of Differential Equations Related to Vector-Valued Jack Polynomials on the Torus 
    Dunkl, C.F. (Symmetry, Integrability and Geometry: Methods and Applications, 2017)
    For each irreducible module of the symmetric group SN there is a set of parametrized nonsymmetric Jack polynomials in N variables taking values in the module. These polynomials are simultaneous eigenfunctions of a commutative ...
  • Orthogonality Measure on the Torus for Vector-Valued Jack Polynomials 
    Dunkl, C.F. (Symmetry, Integrability and Geometry: Methods and Applications, 2016)
    For each irreducible module of the symmetric group on N objects there is a set of parametrized nonsymmetric Jack polynomials in N variables taking values in the module. These polynomials are simultaneous eigenfunctions of ...
  • Polynomials Associated with Dihedral Groups 
    Dunkl, C.F. (Symmetry, Integrability and Geometry: Methods and Applications, 2007)
    There is a commutative algebra of differential-difference operators, with two parameters, associated to any dihedral group with an even number of reflections. The intertwining operator relates this algebra to the algebra ...
  • Some Orthogonal Polynomials in Four Variables 
    Dunkl, C.F. (Symmetry, Integrability and Geometry: Methods and Applications, 2008)
    The symmetric group on 4 letters has the reflection group D₃ as an isomorphic image. This fact follows from the coincidence of the root systems A₃ and D₃. The isomorphism is used to construct an orthogonal basis of polynomials ...
  • Vector Polynomials and a Matrix Weight Associated to Dihedral Groups 
    Dunkl, C.F. (Symmetry, Integrability and Geometry: Methods and Applications, 2014)
    The space of polynomials in two real variables with values in a 2-dimensional irreducible module of a dihedral group is studied as a standard module for Dunkl operators. The one-parameter case is considered (omitting the ...
  • Vector-Valued Jack Polynomials from Scratch 
    Dunkl, C.F.; Luque, J. (Symmetry, Integrability and Geometry: Methods and Applications, 2011)
    Vector-valued Jack polynomials associated to the symmetric group SN are polynomials with multiplicities in an irreducible module of SN and which are simultaneous eigenfunctions of the Cherednik-Dunkl operators with some ...
  • Vector-Valued Polynomials and a Matrix Weight Function with B₂-Action 
    Dunkl, C.F. (Symmetry, Integrability and Geometry: Methods and Applications, 2013)
  • Vector-Valued Polynomials and a Matrix Weight Function with B₂-Action. II 
    Dunkl, C.F. (Symmetry, Integrability and Geometry: Methods and Applications, 2013)
    This is a sequel to [SIGMA 9 (2013), 007, 23 pages], in which there is a construction of a 2×2 positive-definite matrix function K(x) on R². The entries of K(x) are expressed in terms of hypergeometric functions. This ...