Non-Symmetric Jack Polynomials and Integral Kernels
| dc.creator | Baker, T. H. | |
| dc.creator | Forrester, P. J. | |
| dc.date | 1996-12-01 | |
| dc.date.accessioned | 2026-07-07T09:17:21Z | |
| dc.date.available | 2026-07-07T09:17:21Z | |
| dc.description | We investigate some properties of non-symmetric Jack, Hermite and Laguerre polynomials which occur as the polynomial part of the eigenfunctions for certain Calogero-Sutherland models with exchange terms. For the non-symmetric Jack polynomials, the constant term normalization ${\cal N}_η$ is evaluated using recurrence relations, and ${\cal N}_η$ is related to the norm for the non-symmetric analogue of the power-sum inner product. Our results for the non-symmetric Hermite and Laguerre polynomials allow the explicit determination of the integral kernels which occur in Dunkl's theory of integral transforms based on reflection groups of type $A$ and $B$, and enable many analogues of properties of the classical Fourier, Laplace and Hankel transforms to be derived. The kernels are given as generalized hypergeometric functions based on non-symmetric Jack polynomials. Central to our calculations is the construction of operators $\widehatΦ$ and $\widehatΨ$, which act as lowering-type operators for the non-symmetric Jack polynomials of argument $x$ and $x^2$ respectively, and are the counterpart to the raising-type operator $Φ$ introduced recently by Knop and Sahi. | |
| dc.description | LaTeX 2.09, 33 pages | |
| dc.identifier | https://arxiv.org/abs/q-alg/9612003 | |
| dc.identifier | http://arxiv.org/abs/q-alg/9612003 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/153641 | |
| dc.subject | Quantum Algebra | |
| dc.title | Non-Symmetric Jack Polynomials and Integral Kernels | |
| dc.type | text |