The paper argues that the Macdonald triad admits elliptic deformations, but the defining linear equations for elliptic Baker-Akhiezer functions remain ambiguous except at m=1.
Elliptic Deformation of the Gaiotto-Rap\v{c}\'{a}k Corner VOA and the Associated Partially Symmetric Polynomials
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abstract
We construct the elliptic Miura transformation and use it to obtain the expression of the currents of elliptic corner VOA. We subsequently prove a novel combinatorial formula that is essential for deriving the quadratic relations of the currents. In addition, we give a conjecture that relates the correlation function of the currents of elliptic corner VOA to a certain family of partially symmetric polynomials. The elliptic Macdonald polynomials, constructed recently by Awata-Kanno-Mironov-Morozov-Zenkevich, and Fukuda-Ohkubo-Shiraishi, can be obtained as a particular case of this family.
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Elliptic triad
The paper argues that the Macdonald triad admits elliptic deformations, but the defining linear equations for elliptic Baker-Akhiezer functions remain ambiguous except at m=1.