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From Kajihara's transformation formula to deformed Macdonald-Ruijsenaars and Noumi-Sano operators
Chalmers Univ Technol, Dept Math Sci, S-41296 Gothenburg, Sweden.;Univ Gothenburg, S-41296 Gothenburg, Sweden..
KTH, School of Engineering Sciences (SCI), Physics, Condensed Matter Theory.ORCID iD: 0000-0001-7481-2245
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.). Kobe Univ, Dept Math, Kobe, Hyogo 6578501, Japan..ORCID iD: 0000-0001-6003-5908
Chalmers Univ Technol, Dept Math Sci, S-41296 Gothenburg, Sweden.;Univ Gothenburg, S-41296 Gothenburg, Sweden..
2022 (English)In: Selecta Mathematica, New Series, ISSN 1022-1824, E-ISSN 1420-9020, Vol. 28, no 2, article id 24Article in journal (Refereed) Published
Abstract [en]

Kajihara obtained in 2004 a remarkable transformation formula connecting multiple basic hypergeometric series associated with A-type root systems of different ranks. By specialisations of his formula, we deduce kernel identities for deformed Macdonald-Ruijsenaars (MR) and Noumi-Sano (NS) operators. The deformed MR operators were introduced by Sergeev and Veselov in the first order case and by Feigin and Silantyev in the higher order cases. As applications of our kernel identities, we prove that all of these operators pairwise commute and are simultaneously diagonalised by the super-Macdonald polynomials. We also provide an explicit description of the algebra generated by the deformed MR and/or NS operators by a Harish-Chandra type isomorphism and show that the deformed MR (NS) operators can be viewed as restrictions of inverse limits of ordinary MR (NS) operators.

Place, publisher, year, edition, pages
Springer Nature , 2022. Vol. 28, no 2, article id 24
Keywords [en]
Macdonald-Ruijsenaars operators, Noumi-Sano operators, Multiple basic hypergeometric series, Kernel identities
National Category
Mathematical Analysis
Identifiers
URN: urn:nbn:se:kth:diva-307293DOI: 10.1007/s00029-021-00745-zISI: 000736590000007Scopus ID: 2-s2.0-85122077819OAI: oai:DiVA.org:kth-307293DiVA, id: diva2:1630519
Note

QC 20220120

Available from: 2022-01-20 Created: 2022-01-20 Last updated: 2022-06-25Bibliographically approved

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Langmann, EdwinNoumi, Masatoshi

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