Evaluation of Nonsymmetric Macdonald Superpolynomials at Special Points

  title={Evaluation of Nonsymmetric Macdonald Superpolynomials at Special Points},
  author={Charles F. Dunkl},
  • C. Dunkl
  • Published 1 April 2021
  • Mathematics
  • Symmetry
In a preceding paper the theory of nonsymmetric Macdonald polynomials taking values in modules of the Hecke algebra of type A (Dunkl and Luque SLC 2012) was applied to such modules consisting of polynomials in anti-commuting variables, to define nonsymmetric Macdonald superpolynomials. These polynomials depend on two parameters q,t and are defined by means of a Yang–Baxter graph. The present paper determines the values of a subclass of the polynomials at the special points 1,t,t2,… or 1,t−1,t−2… 


Nonsymmetric Macdonald Superpolynomials
  • C. Dunkl
  • Mathematics
    Symmetry, Integrability and Geometry: Methods and Applications
  • 2020
There are representations of the type-A Hecke algebra on spaces of polynomials in anti-commuting variables. Luque and the author [Sém. Lothar. Combin. 66 (2012), Art. B66b, 68 pages, arXiv:1106.0875]
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