Nonsymmetric Macdonald Superpolynomials

@article{Dunkl2020NonsymmetricMS,
  title={Nonsymmetric Macdonald Superpolynomials},
  author={Charles F. Dunkl},
  journal={Symmetry, Integrability and Geometry: Methods and Applications},
  year={2020}
}
  • C. Dunkl
  • Published 11 November 2020
  • Mathematics
  • Symmetry, Integrability and Geometry: Methods and Applications
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] constructed nonsymmetric Macdonald polynomials taking values in arbitrary modules of the Hecke algebra. In this paper the two ideas are combined to define and study nonsymmetric Macdonald polynomials taking values in the aforementioned anti-commuting polynomials, in other words, superpolynomials… 

Evaluation of Nonsymmetric Macdonald Superpolynomials at Special Points

TLDR
The values of a subclass of the polynomials at the special points 1,t,t2,… or 1, t−1,t−2,….

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Nonsymmetric Macdonald polynomials

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In a previous paper J.-G. Luque and the author (Sem. Loth. Combin. 2011) developed the theory of nonsymmetric Macdonald polynomials taking values in an irreducible module of the Hecke algebra of the