Vector-Valued Jack Polynomials from Scratch

  title={Vector-Valued Jack Polynomials from Scratch},
  author={Charles F. Dunkl and Jean-Gabriel Luque},
  journal={Symmetry Integrability and Geometry-methods and Applications},
  • C. DunklJ. Luque
  • Published 13 September 2010
  • Mathematics
  • Symmetry Integrability and Geometry-methods and Applications
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 additional properties concerning the leading monomial. These polynomials were introduced by Griffeth in the general setting of the complex reflections groups G(r;p;N) and studied by one of the authors (C. Dunkl) in the specialization r = p = 1 (i.e. for the symmetric group). By… 

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