Letters in Mathematical Physics

, Volume 34, Issue 1, pp 1–8 | Cite as

A quantum dual pair\(\mathfrak{s}\mathfrak{l}_2 ,\mathfrak{o}_n \) and the associated Capelli identity

  • Masatoshi Noumi
  • Tôru Umeda
  • Masato Wakayama


A quantum analogue of the dual pair\(\mathfrak{s}\mathfrak{l}_2 ,\mathfrak{o}_n \) is introduced in terms of the oscillator representation of U q \((\mathfrak{s}\mathfrak{l}_2 )\). Its commutant and the associated identity of Capelli type are discussed.

Mathematics Subject Classifications (1991)

17B37 81R50 


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Copyright information

© Kluwer Academic Publishers 1995

Authors and Affiliations

  • Masatoshi Noumi
    • 1
  • Tôru Umeda
    • 2
  • Masato Wakayama
    • 3
  1. 1.Department of Mathematical SciencesUniversity of TokyoKomaba, Megro-ku, TokyoJapan
  2. 2.Department of MathematicsFaculty of Science, Kyoto UniversityKyotoJapan
  3. 3.Department of MathematicsFaculty of General Education, Tottori UniversityTottoriJapan

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