Macdonald polynomials and cyclic sieving

نویسندگان

چکیده

The Garsia–Haiman module is a bigraded Sn-module whose Frobenius image Macdonald polynomial. method of orbit harmonics promotes an Sn-set X to graded polynomial ring. can be applied prove cyclic sieving phenomena which notion that encapsulates the fixed-point structure finite group action on set. By applying this idea module, we provide results regarding enumeration matrices are invariant under certain row and column rotation translation entries.

برای دانلود باید عضویت طلایی داشته باشید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Macdonald Polynomials and Geometry

We explain some remarkable connections between the twoparameter symmetric polynomials discovered in 1988 by Macdonald, and the geometry of certain algebraic varieties, notably the Hilbert scheme Hilb(C 2 ) of points in the plane, and the variety Cn of pairs of commuting n× n matrices.

متن کامل

Cyclic Sieving for Cyclic Codes

These are notes on a preliminary follow-up to a question of Jim Propp, about cyclic sieving of cyclic codes. We show that two of the Mahonian polynomials are cyclic sieving polynomials for certain Dual Hamming Codes: X and X inv for q = 2, 3 and q = 2, respectively.

متن کامل

Factorisation 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 کامل

Macdonald Polynomials and Algebraic Integrability

We construct explicitly (non-polynomial) eigenfunctions of the difference operators by Macdonald in case t = q, k ∈ Z. This leads to a new, more elementary proof of several Macdonald conjectures, first proved by Cherednik. We also establish the algebraic integrability of Macdonald operators at t = q (k ∈ Z), generalizing the result of Etingof and Styrkas. Our approach works uniformly for all ro...

متن کامل

Vector 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 کامل

ذخیره 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: European Journal of Combinatorics

سال: 2022

ISSN: ['1095-9971', '0195-6698']

DOI: https://doi.org/10.1016/j.ejc.2021.103465