相关论文: A characterization of interpolation Macdonald poly…

For any admissible pair of irreducible reduced crystallographic root systems, we present discrete orthogonality relations for a finite-dimensional system of Macdonald polynomials with parameters on the unit circle subject to a truncation…

We prove a generalisation to any characteristic of a result of Macdonald that describes strict polynomial functors in characteristic zero in terms of representations of the groupoid of finite sets and bijections. Our result will give an…

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 eigenfunctions of Cherednik operators. Several…

Generalized Macdonald polynomials (GMP) are eigenfunctions of specifically-deformed Ruijsenaars Hamiltonians and are built as triangular polylinear combinations of Macdonald polynomials. They are orthogonal with respect to a modified scalar…

Uniform interpolation is the property that, for any formula and set of atoms, there exists the strongest consequence omitting those atoms. It plays a central role in knowledge representation and reasoning tasks such as knowledge update and…

We present an explicit difference operator diagonalized by the Macdonald polynomials associated with an (arbitrary) admissible pair of irreducible reduced crystallographic root systems. By the duality symmetry, this gives rise to an…

We present an explicit formula for the transition matrix $\mathcal{C}$ from the type $C_n$ degeneration of the Koornwinder polynomials $P_{(1^r)}(x\,|\,a,-a,c,-c\,|\,q,t)$ with one column diagrams, to the type $C_n$ monomial symmetric…

Macdonald symmetric polynomial at $t=q^{-m}$ reduces to a sum of much simpler complementary non-symmetric polynomials, which satisfy a simple system of the first order linear difference equations with constant coefficients, much simpler…

Macdonald superpolynomials provide a remarkably rich generalization of the usual Macdonald polynomials. The starting point of this work is the observation of a previously unnoticed stability property of the Macdonald superpolynomials when…

In this paper, we study the representations of integral quadratic polynomials. Particularly, it is shown that there are only finitely many equivalence classes of positive ternary universal integral quadratic polynomials, and that there are…

This is a paper about $c$-functions and Macdonald polynomials. There are $c$-function formulas for $E$-expansions of $P_\lambda$ and $A_{\lambda+\rho}$, principal specializations of $P_\lambda$ and $E_\mu$, for Macdonald's constant term…

We construct an integral representation of eigenfunctions for Macdonald's $q$-difference operator associated with the root system of type $C_n .$ It is given in terms of a restriction of a $q$-Jordan-Pochhammer integral. Choosing a suitable…

We introduce generalization of famous Macdonald polynomials for the case of super-Young diagrams that contain half-boxes on the equal footing with full boxes. These super-Macdonald polynomials are polynomials of extended set of variables:…

We show how a certain limit of the nonsymmetric Macdonald polynomials appears in the representation theory of semisimple groups over p--adic fields as matrix coefficients for the unramified principal series representations. The result is…

In this paper some classes of local polynomial functions on abelian groups are characterized by the properties of their variety. For this characterization we introduce a numerical quantity depending on the variety of the local polynomial…

In this article we give a combinatorial formula for a certain class of Koornwinder polynomials, also known as Macdonald polynomials of type $\tilde{C}$. In particular, we give a combinatorial formula for the Koornwinder polynomials…

The main goal of this paper is to categorify the specialized parasymmetric (intermediate) Macdonald polynomials. These polynomials depend on a parabolic subalgebra of a simple Lie algebra and generalize the symmetric and nonsymmetric…

Macdonald polynomials are an important class of symmetric functions, with connections to many different fields. Etingof and Kirillov showed an intimate connection between these functions and representation theory: they proved that Macdonald…

In the basic representation of $U_q(\hat{sl}(2))$ realized via the algebra of symmetric functions we compare the canonical basis with the basis of Macdonald polynomials with $q=t^2$. We show that the Macdonald polynomials are invariant with…

We study Macdonald polynomials from a basic hypergeometric series point of view. In particular, we show that the Pieri formula for Macdonald polynomials and its recently discovered inverse, a recursion formula for Macdonald polynomials,…