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BC infinity Calogero-Moser operator and super Jacobi polynomials
journal contribution
posted on 2014-11-10, 14:00 authored by A.N. Sergeev, Alexander VeselovAlexander VeselovAn 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.
Funding
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.
History
School
- Science
Department
- Mathematical Sciences
Published in
ADVANCES IN MATHEMATICSVolume
222Issue
5Pages
1687 - 1726 (40)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.Publisher
© Elsevier IncVersion
- VoR (Version of Record)
Publication date
2009Notes
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-licenseISSN
0001-8708Publisher version
Language
- en