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Construction of Eigenfunctions for the Elliptic Ruijsenaars Difference Operators
KTH, School of Engineering Sciences (SCI), Physics.ORCID iD: 0000-0001-7481-2245
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).
Graduate School of Mathematical Sciences, The University of Tokyo, Komaba, Tokyo, 153-8914, Japan.
2022 (English)In: Communications in Mathematical Physics, ISSN 0010-3616, E-ISSN 1432-0916, Vol. 391, no 3, p. 901-950Article in journal (Refereed) Published
Abstract [en]

We present a perturbative construction of two kinds of eigenfunctions of the commuting family of difference operators defining the elliptic Ruijsenaars system. The first kind corresponds to elliptic deformations of the Macdonald polynomials, and the second kind generalizes asymptotically free eigenfunctions previously constructed in the trigonometric case. We obtain these eigenfunctions as infinite series which, as we show, converge in suitable domains of the variables and parameters. Our results imply that, for the domain where the elliptic Ruijsenaars operators define a relativistic quantum mechanical system, the elliptic deformations of the Macdonald polynomials provide a family of orthogonal functions with respect to the pertinent scalar product. 

Place, publisher, year, edition, pages
Springer Nature , 2022. Vol. 391, no 3, p. 901-950
National Category
Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-321870DOI: 10.1007/s00220-021-04195-8ISI: 000767904000001Scopus ID: 2-s2.0-85126108313OAI: oai:DiVA.org:kth-321870DiVA, id: diva2:1713538
Note

QC 20221125

Available from: 2022-11-25 Created: 2022-11-25 Last updated: 2022-11-25Bibliographically approved

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Langmann, EdwinNoumi, Masatoshi

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