From Kajihara’s transformation formula to deformed Macdonald–Ruijsenaars and Noumi–Sano operators
Artikel i vetenskaplig tidskrift, 2022

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.

Macdonald–Ruijsenaars operators

Multiple basic hypergeometric series

Noumi–Sano operators

Kernel identities

Författare

Martin Hallnäs

Chalmers, Matematiska vetenskaper, Analys och sannolikhetsteori

Göteborgs universitet

Edwin Langmann

Kungliga Tekniska Högskolan (KTH)

Masatoshi Noumi

Kobe University

Kungliga Tekniska Högskolan (KTH)

Hjalmar Rosengren

Göteborgs universitet

Chalmers, Matematiska vetenskaper, Analys och sannolikhetsteori

Selecta Mathematica, New Series

1022-1824 (ISSN) 14209020 (eISSN)

Vol. 28 2 24

Kvasi-invarianter för ändliga Coxeter-grupper och integrabla system

Vetenskapsrådet (VR) (2018-04291), 2019-01-01 -- 2022-12-31.

Ämneskategorier

Geometri

Matematisk analys

DOI

10.1007/s00029-021-00745-z

Mer information

Senast uppdaterat

2022-01-20