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Elliptic Deformation of the Gaiotto-Rapčák Corner VOA and the Associated Partially Symmetric Polynomials (2406.15860v3)

Published 22 Jun 2024 in hep-th, math-ph, math.CO, math.MP, math.QA, and math.RT

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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