Year: 2008
Type: preprint
Abstract: An infinite-dimensional version of Calogero-Moser operator of $BC$-type and the corresponding Jacobi symmetric functions are introduced and studied, including the analogues of Pieri formula and Okounkov's binomial formula. We use this to describe all the ideals linearly generated by the Jacobi symmetric functions and show that the deformed $BC(m,n)$ Calogero-Moser operators, introduced in our earlier work, appear here in a natural way as the restrictions of the $BC_{\infty}$ operator to the corresponding finite-dimensional subvarieties. As a corollary we have the integrability of these quantum systems and all the main formulas for the related super Jacobi polynomials.
Source: arXiv (Cornell University)
Authors: Sergeev, A. N., Veselov, A. P.
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4394658052