Page Manager: Webmaster
Last update: 9/11/2012 3:13 PM
| Authors |
F. Atai Martin Hallnäs E. Langmann |
|---|---|
| Published in | Bulletin of the London Mathematical Society |
| Volume | 51 |
| Issue | 2 |
| Pages | 353-370 |
| ISSN | 0024-6093 |
| Publication year | 2019 |
| Published at |
Department of Mathematical Sciences |
| Pages | 353-370 |
| Language | en |
| Links |
dx.doi.org/10.1112/blms.12234 |
| Keywords | integrability, Mathematics |
| Subject categories | Geometry |
We prove orthogonality and compute explicitly the (quadratic) norms for super-Jack polynomials SP lambda((z1, horizontal ellipsis ,zn),(w1, horizontal ellipsis ,wm);theta) with respect to a natural positive semi-definite, but degenerate, Hermitian product ⟨center dot,center dot⟩n,m,theta '. In case m=0 (or n=0), our product reduces to Macdonald's well-known inner product ⟨center dot,center dot⟩n,theta ', and we recover his corresponding orthogonality results for the Jack polynomials P lambda((z1, horizontal ellipsis ,zn);theta). From our main results, we readily infer that the kernel of ⟨center dot,center dot⟩n,m,theta ' is spanned by the super-Jack polynomials indexed by a partition lambda not containing the mxn rectangle (mn). As an application, we provide a Hilbert space interpretation of the deformed trigonometric Calogero-Moser-Sutherland operators of type A(n-1,m-1).
© UNIVERSITY OF GOTHENBURG • Sweden • Box 100 • SE-405 30 Gothenburg
Phone: +46 31 786 0000 • Contact • Organisation number: 202100-3153
About the website
Facebook
Twitter
Instagram
Youtube
Weibo