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BC infinity Calogero-Moser operator and super Jacobi polynomials

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journal contribution
posted on 10.11.2014 by A.N. Sergeev, Alexander Veselov
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.

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 MATHEMATICS

Volume

222

Issue

5

Pages

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 Inc

Version

VoR (Version of Record)

Publication date

2009

Notes

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

ISSN

0001-8708

Language

en

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