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arXiv · 2106.14919

Elliptic Ruijsenaars difference operators, symmetric polynomials, and Wess-Zumino-Witten fusion rings

Jan Felipe van Diejen·Tamás Görbe
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Abstract

The fusion ring for $\widehat{\mathfrak{su}}(n)_m$ Wess-Zumino-Witten conformal field theories is known to be isomorphic to a factor ring of the ring of symmetric polynomials presented by Schur polynomials. We introduce a deformation of this factor ring associated with eigenpolynomials for the elliptic Ruijsenaars difference operators. The corresponding Littlewood-Richardson coefficients are governed by a Pieri rule stemming from the eigenvalue equation. The orthogonality of the eigenbasis gives rise to an analog of the Verlinde formula. In the trigonometric limit, our construction recovers the refined $\widehat{\mathfrak{su}}(n)_m$ Wess-Zumino-Witten fusion ring associated with the Macdonald polynomials.

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BibTeXRIS

Jan Felipe van Diejen, Tamás Görbe. 2021-06-28. Elliptic Ruijsenaars difference operators, symmetric polynomials, and Wess-Zumino-Witten fusion rings. https://doi.org/10.1007/s00029-023-00883-6

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