## 5 Citations

### Evaluation of Nonsymmetric Macdonald Superpolynomials at Special Points

- MathematicsSymmetry
- 2021

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

### 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]…

### On the Hopf algebra of noncommutative symmetric functions in superspace

- Mathematics
- 2022

We study in detail the Hopf algebra of noncommutative symmetric functions in superspace sNSym , introduced by Fishel, Lapointe and Pinto. We introduce a family of primitive elements of sNSym and…

### Symmetric functions in superspace: a compendium of results and open problems (including a SageMath worksheet)

- Mathematics
- 2019

We present a review of the most important results in the theory of symmetric functions in superspace (or symmetric superpolynomials), summarizing all principal contributions since its introduction in…

### $m$-Symmetric functions, non-symmetric Macdonald polynomials and positivity conjectures

- Mathematics
- 2022

We study the space, Rm, of m-symmetric functions consisting of polynomials that are symmetric in the variables xm+1, xm+2, xm+3, . . . but have no special symmetry in the variables x1, . . . , xm. We…

## References

SHOWING 1-10 OF 26 REFERENCES

### Further Pieri-type formulas for the nonsymmetric Macdonald polynomial

- Mathematics
- 2010

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

- Mathematics
- 1999

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

- MathematicsAnnales Henri Poincaré
- 2019

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

- 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…

### Affine Hecke algebras and raising operators for Macdonald polynomials

- Mathematics
- 1996

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

- Mathematics
- 2012

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

- Mathematics
- 2010

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

- 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…

### Classical symmetric functions in superspace

- Mathematics, Computer Science
- 2006

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

- 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…