# Evaluation of Nonsymmetric Macdonald Superpolynomials at Special Points

@article{Dunkl2021EvaluationON, title={Evaluation of Nonsymmetric Macdonald Superpolynomials at Special Points}, author={Charles F. Dunkl}, journal={Symmetry}, year={2021}, volume={13}, pages={779} }

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…

## References

SHOWING 1-9 OF 9 REFERENCES

Nonsymmetric Macdonald Superpolynomials

- MathematicsSymmetry, 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]…

Vector valued Macdonald polynomials

- Mathematics
- 2011

This paper defines and investigates nonsymmetric Macdonald polynomials with values in an irreducible module of the Hecke algebra of type $A_{N-1}$. These polynomials appear as simultaneous…

Macdonald polynomials in superspace as eigenfunctions of commuting operators

- Mathematics
- 2012

A generalization of the Macdonald polynomials depending upon both commuting and anticommuting variables has been introduced recently. The construction relies on certain orthogonality and…

Clustering properties of rectangular Macdonald polynomials

- Mathematics
- 2012

The clustering properties of Jack polynomials are relevant in the theoretical study of the fractional Hall states. In this context, some factorization properties have been conjectured for the…

A q-analogue of the type A Dunkl operator and integral kernel

- Mathematics
- 1997

We introduce the $q$-analogue of the type $A$ Dunkl operators, which are a set of degree--lowering operators on the space of polynomials in $n$ variables. This allows the construction of…

The norm and the Evaluation of the Macdonald polynomials in superspace

- MathematicsEur. J. Comb.
- 2020

Symmetric Jack polynomials from non-symmetric theory

- Mathematics, Computer Science
- 1997

It is shown that orthogonality relations, normalization formulas, a specialization formula and the evaluation of a proportionality constant relating the anti-symmetric Jack polynomials to a product of differences multiplied by the symmetric Jack coefficients with a shifted parameter can be derived from knowledge of their corresponding properties.

Cyclotomic double affine Hecke algebras

- Mathematics
- 2020

We show that the partially spherical cyclotomic rational Cherednik algebra (obtained from the full rational Cherednik algebra by averaging out the cyclotomic part of the underlying reflection group)…