A direct approach to the bispectral problem for the Ruijsenaars-Macdonald q-difference operators

2012/06/23 by Noumi, Masatoshi, Shiraishi, Jun'ichi · 3 citations
#FOS: Mathematics #Quantum Algebra (math.QA)

paper · doi:10.48550/arxiv.1206.5364

Abstract

We present a direct approach to the bispectral problem associated with the Ruijsenaars-Macdonald q-difference operators of GL type. We give an explicit construction of the meromorphic function psi_n(x;s|q,t) on Tⁿ_x Tⁿ_s, which is the solution of the bispectral problem up to a certain gauge transformation. Some basic properties of psi_n(x;s|q,t) are studied, including the structure of the divisor of poles, the symmetries psi_n(x;s|q,t)=psi_n(s;x|q,t)=psi_n(x;s|q,q/t), and the recursive structure described in terms of Jackson integrals or q-difference operators.

Cited by

• Slant sums of quiver gauge theories
• Baker-Akhiezer specialisation of joint eigenfunctions for hyperbolic relativistic Calogero-Moser Hamiltonians
• Calogero-Sutherland hyperbolic system and Heckman-Opdam \mathfrakgl_n hypergeometric function

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