The norm and the Evaluation of the Macdonald polynomials in superspace

@article{Gonzlez2020TheNA,
  title={The norm and the Evaluation of the Macdonald polynomials in superspace},
  author={Camilo Gonz{\'a}lez and Luc Lapointe},
  journal={Eur. J. Comb.},
  year={2020},
  volume={83}
}

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References

SHOWING 1-10 OF 26 REFERENCES

Further Pieri-type formulas for the nonsymmetric Macdonald polynomial

The branching coefficients in the expansion of the elementary symmetric function multiplied by a symmetric Macdonald polynomial Pκ(z) are known explicitly. These formulas generalise the known r=1

Symmetric and nonsymmetric Macdonald polynomials

The symmetric Macdonald polynomials may be constructed from the nonsymmetric Macdonald polynomials. This allows us to develop the theory of the symmetric Macdonald polynomials by first developing the

Pieri Rules for the Jack Polynomials in Superspace and the 6-Vertex Model

We present Pieri rules for the Jack polynomials in superspace. The coefficients in the Pieri rules are, except for an extra determinant, products of quotients of linear factors in $$\alpha $$α

Clustering properties of rectangular Macdonald polynomials

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

Affine Hecke algebras and raising operators for Macdonald polynomials

We introduce certain raising and lowering operators for Macdonald polynomials (of type $A_{n-1}$) by means of Dunkl operators. The raising operators we discuss are a natural $q$-analogue of raising

Macdonald Polynomials in Superspace: Conjectural Definition and Positivity Conjectures

We introduce a conjectural construction for an extension to superspace of the Macdonald polynomials. The construction, which depends on certain orthogonality and triangularity relations, is tested

SOME PROPERTIES OF MACDONALD POLYNOMIALS WITH PRESCRIBED SYMMETRY

he Macdonald polynomials with prescribed symmetry are obtained from the non-symmetric Macdonald polynomials via the operations of t-symmetrization, t-antisymmetrization and normalization. Motivated

Macdonald polynomials in superspace as eigenfunctions of commuting operators

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

Classical symmetric functions in superspace

TLDR
Various basic results, such as the generating functions for the multiplicative bases, Cauchy formulas, involution operations as well as the combinatorial scalar product are also generalized.

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

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