• Corpus ID: 9798067

Symmetric and Antisymmetric Vector-valued Jack Polynomials

@article{Dunkl2010SymmetricAA,
  title={Symmetric and Antisymmetric Vector-valued Jack Polynomials},
  author={Charles F. Dunkl},
  journal={arXiv: Combinatorics},
  year={2010}
}
  • C. Dunkl
  • Published 25 January 2010
  • Mathematics
  • arXiv: Combinatorics
Polynomials with values in an irreducible module of the symmetric group can be given the structure of a module for the rational Cherednik algebra, called a standard module. This algebra has one free parameter and is generated by differential-difference ("Dunkl") operators, multiplication by coordinate functions and the group algebra. By specializing Griffeth's (arXiv:0707.0251) results for the G(r,p,n) setting, one obtains norm formulae for symmetric and antisymmetric polynomials in the… 

Orthogonality Measure on the Torus for Vector-Valued Jack Polynomials

For each irreducible module of the symmetric group on N objects there is a set of parametrized nonsymmetric Jack polynomials in N variables taking values in the module. These polynomials are

Vector-Valued Jack Polynomials from Scratch

Vector-valued Jack polynomials associated to the symmetric group SN are polynomials with multiplicities in an irreducible module of SN and which are simultaneous eigenfunctions of the Cherednik{Dunkl

Vector-valued Jack polynomials and wavefunctions on the torus

The Hamiltonian of the quantum Calogero–Sutherland model of N identical particles on the circle with 1/r2 interactions has eigenfunctions consisting of Jack polynomials times the base state. By use

2 Yang – Baxter type graph associated to a partition 2 . 1 Sorting a vector

Vector-valued Jack polynomials associated to the symmetric group SN are polynomials with multiplicities in an irreducible module of SN and which are simultaneous eigenfunctions of the Cherednik–Dunkl

A Linear System of Differential Equations Related to Vector-Valued Jack Polynomials on the Torus

For each irreducible module of the symmetric group $\mathcal{S}_{N}$ there is a set of parametrized nonsymmetric Jack polynomials in $N$ variables taking values in the module. These polynomials are

Generalized Jack polynomials and the representation theory of rational Cherednik algebras

We apply the Dunkl–Opdam operators and generalized Jack polynomials to study category $${{\mathcal O}_c}$$ for the rational Cherednik algebra of type G(r, p, n). We determine the set of aspherical

Macdonald polynomials as characters of Cherednik algebra modules

We prove that Macdonald polynomials are characters of irreducible Cherednik algebra modules.

Macdonald polynomials as characters of Cherednik algebra modules

We prove that Macdonald polynomials are characters of irreducible Cherednik algebra modules.

References

SHOWING 1-10 OF 12 REFERENCES

Orthogonal functions generalizing Jack polynomials

The rational Cherednik algebra ℍ is a certain algebra of differential-reflection operators attached to a complex reflection group W and depending on a set of central parameters. Each irreducible

Symmetric Jack polynomials from non-symmetric theory

It is shown that orthogonality relations, normalization formulas, a specialization formula and the evaluation of a proportionality constant relating the anti-symmetric Jack polynomials to a product of differences multiplied by the symmetric Jack coefficients with a shifted parameter can be derived from knowledge of their corresponding properties.

Unitary representations of rational Cherednik algebras

We study unitarity of lowest weight irreducible representations of rational Cherednik algebras. We prove several general results, and use them to determine which lowest weight representations are

Parabolic induction and restriction functors for rational Cherednik algebras

Abstract.We introduce parabolic induction and restriction functors for rational Cherednik algebras, and study their basic properties. Then we discuss applications of these functors to representation

Symmetric functions and Hall polynomials

I. Symmetric functions II. Hall polynomials III. HallLittlewood symmetric functions IV. The characters of GLn over a finite field V. The Hecke ring of GLn over a finite field VI. Symmetric functions

A New Approach to the Representation Theory of the Symmetric Groups. II

The present paper is a revised Russian translation of the paper “A new approach to representation theory of symmetric groups,” Selecta Math., New Series, 2, No. 4, 581–605 (1996). Numerous

Dunkl operators, Bessel functions and the discriminant of a finite Coxeter group

Toute utilisation commerciale ou impression systématique est constitutive d’une infraction pénale, toute copie ou impressions de ce fichier doit contenir la présente mention de copyright.

Orthogonal Polynomials of Several Variables

Results parallel to the theory of orthogonal polynomials in one variable are established using a vectormatrix notation, which reports on the recent development on the general theory of hospitalisation in several variables.

Rational Cherednik algebras and Hilbert schemes