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Search: swepub > Rosengren Hjalmar 1972 > Langmann Edwin

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1.
  • Hallnäs, Martin, 1979, et al. (author)
  • Higher Order Deformed Elliptic Ruijsenaars Operators
  • 2022
  • In: Communications in Mathematical Physics. - : Springer Science and Business Media LLC. - 0010-3616 .- 1432-0916. ; 392
  • Journal article (peer-reviewed)abstract
    • We present four infinite families of mutually commuting difference operators which include the deformed elliptic Ruijsenaars operators. The trigonometric limit of this kind of operators was previously introduced by Feigin and Silantyev. They provide a quantum mechanical description of two kinds of relativistic quantum mechanical particles which can be identified with particles and anti-particles in an underlying quantum field theory. We give direct proofs of the commutativity of our operators and of some other fundamental properties such as kernel function identities. In particular, we give a rigorous proof of the quantum integrability of the deformed Ruijsenaars model.
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2.
  • Hallnäs, Martin, 1979, et al. (author)
  • From Kajihara’s transformation formula to deformed Macdonald–Ruijsenaars and Noumi–Sano operators
  • 2022
  • In: Selecta Mathematica, New Series. - : Springer Science and Business Media LLC. - 1420-9020 .- 1022-1824. ; 28:2
  • Journal article (peer-reviewed)abstract
    • 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.
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  • Result 1-2 of 2
Type of publication
journal article (2)
Type of content
peer-reviewed (2)
Author/Editor
Rosengren, Hjalm... (2)Undo refine
Langmann, Edwin (2)Undo refine
Hallnäs, Martin, 197 ... (2)
Noumi, Masatoshi (2)
University
University of Gothenburg (2)
Royal Institute of Technology (2)
Chalmers University of Technology (2)
Language
English (2)
Research subject (UKÄ/SCB)
Natural sciences (2)
Year
2022 (2)

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