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Title: BC infinity Calogero-Moser operator and super Jacobi polynomials
Authors: Sergeev, A.N.
Veselov, A.P.
Keywords: Calogero–Moser systems
Symmetric functions
Jacobi polynomials
Issue Date: 2009
Publisher: © Elsevier Inc
Citation: SERGEEV, A.N. and VESELOV, A.P., 2009. BC infinity Calogero-Moser operator and super Jacobi polynomials. Advances in Mathematics, 222 (5), pp. 1687 - 1726.
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)BC(m,n) Calogero–Moser operators, introduced in our earlier work, appear here in a natural way as the restrictions of the BC∞BC∞ 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.
Description: This is the published version of an article that appeared in the journal, Advances in Mathematics [© Elsevier Inc ]. It is published in an Open Archive under an Elsevier user license. Details of this licence are available here: http://www.elsevier.com/about/open-access/open-access-policies/oa-license-policy/elsevier-user-license
Sponsor: This work has been partially supported by EPSRC (grant EP/E004008/1) and by the European Union through the FP6 Marie Curie RTN ENIGMA (contract number MRTN-CT-2004-5652) and through ESF programme MISGAM.
Version: Published
DOI: 10.1016/j.aim.2009.06.014
URI: https://dspace.lboro.ac.uk/2134/16203
Publisher Link: http://dx.doi.org/10.1016/j.aim.2009.06.014
ISSN: 0001-8708
Appears in Collections:Published Articles (Maths)

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