Expanding the quasisymmetric Macdonald polynomials in the fundamental basis
نویسندگان
چکیده
The quasisymmetric Macdonald polynomials G γ (X;q,t) were recently introduced by the first and second authors with Haglund, Mason, Williams in [3] to refine symmetric P λ property that (X;0,0) equals QS (X), Schur polynomial of [9]. We derive an expansion for fundamental basis functions.
منابع مشابه
Breakthroughs in the theory of Macdonald polynomials.
I n 1998, I. G. Macdonald (1) introduced a remarkable new basis for the space of symmetric functions. The elements of this basis are denoted P (x ; q, t), where is a partition and p, q are two free parameters. The P (x ; q, t)’s, which are now called ‘‘Macdonald polynomials,’’ specialize to many of the well known bases for the symmetric functions, by suitable choices of the parameters q and t. ...
متن کاملFactorisation of Macdonald polynomials
1. Macdonald polynomials Macdonald polynomials P λ (x; q, t) are orthogonal symmetric polynomials which are the natural multivariable generalisation of the continuous q-ultraspherical polyno-mials C n (x; β|q) [2] which, in their turn, constitute an important class of hyper-geometric orthogonal polynomials in one variable. Polynomials C n (x; β|q) can be obtained from the general Askey-Wilson p...
متن کاملVector Valued Macdonald Polynomials
This paper defines and investigates nonsymmetric Macdonald polynomials with values in an irreducible module of the Hecke algebra of type AN−1. These polynomials appear as simultaneous eigenfunctions of Cherednik operators. Several objects and properties are analyzed, such as the canonical bilinear form which pairs polynomials with those arising from reciprocals of the original parameters, and t...
متن کاملA probabilistic interpretation of the Macdonald polynomials
The two-parameter Macdonald polynomials are a central object of algebraic combinatorics and representation theory. We give a Markov chain on partitions of k with eigenfunctions the coefficients of the Macdonald polynomials when expanded in the power sum polynomials. The Markov chain has stationary distribution a new two-parameter family of measures on partitions, the inverse of the Macdonald we...
متن کاملA combinatorial model for the Macdonald polynomials.
We introduce a polynomial C(mu)[Z; q, t], depending on a set of variables Z = z(1), z(2),..., a partition mu, and two extra parameters q, t. The definition of C(mu) involves a pair of statistics (maj(sigma, mu), inv(sigma, mu)) on words sigma of positive integers, and the coefficients of the z(i) are manifestly in N[q,t]. We conjecture that C(mu)[Z; q, t] is none other than the modified Macdona...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Algebraic combinatorics
سال: 2023
ISSN: ['2589-5486']
DOI: https://doi.org/10.5802/alco.289