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

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.

21 pages

References in corpus (5)

• The supersymmetric Ruijsenaars-Schneider model
• The Verlinde formula for Higgs bundles
• Duality in elliptic Ruijsenaars system and elliptic symmetric functions
• Construction of eigenfunctions for the elliptic Ruijsenaars difference operators
• Elliptic Ruijsenaars difference operators on bounded partitions

Cited by in corpus (1)

• On refined Chern-Simons and refined ABJ matrix models