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Title:
Elliptic Ruijsenaars operators and WZW fusion rings
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Abstract:
The fusion ring for 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 su(n)_m Wess-Zumino-Witten fusion ring associated with the Macdonald polynomials. This talk is based on joint work with Tamás Görbe, University of Groningen
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