BC infinity Calogero-Moser operator and super Jacobi polynomials
journal contributionposted on 10.11.2014 by A.N. Sergeev, Alexander Veselov
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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.
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.
- Mathematical Sciences