Non-Stationary Ruijsenaars Functions for κ = t⁻¹ᐟᴺ and Intertwining Operators of Ding-Iohara-Miki Algebra

• Veröffentlicht in: Symmetry, Integrability and Geometry: Methods and Applications
• Datum: 2020
• ISSN: 1815-0659
• Hauptverfasser: Fukuda, Masayuki, Ohkubo, Yusuke, Shiraishi, Jun'ichi
• Format: Artikel
• Sprache: Englisch
• Veröffentlicht: Інститут математики НАН України 2020
• Online Zugang: https://nasplib.isofts.kiev.ua/handle/123456789/211004
• Назва журналу: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Zitieren: Non-Stationary Ruijsenaars Functions for κ = t⁻¹ᐟᴺ and Intertwining Operators of Ding-Iohara-Miki Algebra. Masayuki Fukuda, Yusuke Ohkubo and Jun'ichi Shiraishi. SIGMA 16 (2020), 116, 55 pages

We construct the non-stationary Ruijsenaars functions (affine analogue of the Macdonald functions) in the special case κ=t⁻¹ᐟᴺ, using the intertwining operators of the Ding-Iohara-Miki algebra (DIM algebra) associated with -fold Fock tensor spaces. By the -duality of the intertwiners, another expression is obtained for the non-stationary Ruijsenaars functions with κ = t⁻¹ᐟᴺ, which can be regarded as a natural elliptic lift of the asymptotic Macdonald functions to the multivariate elliptic hypergeometric series. We also investigate some properties of the vertex operator of the DIM algebra appearing in the present algebraic framework: an integral operator which commutes with the elliptic Ruijsenaars operator, and the degeneration of the vertex operators to the Virasoro primary fields in the conformal limit → 1.