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- Title
Genus Zero su^(n)m Wess–Zumino–Witten Fusion Rules Via Macdonald Polynomials.
- Authors
van Diejen, J. F.
- Abstract
The Kac–Walton formula computes the fusion coefficients of genus zero su ^ (n) m Wess–Zumino–Witten conformal field theories as the structure constants of the fusion algebra in the basis of Schur polynomials. Modulo a relation identifying the nth elementary symmetric polynomial with the unit polynomial, this fusion algebra is obtained from the algebra of symmetric polynomials in n variables by modding out a fusion ideal generated by the Schur polynomials of degree m + 1 . The present work constructs a refinement of the fusion algebra associated with the Macdonald polynomials at q m t n = 1 . The pertinent refined structure constants turn out to be given by the corresponding parameter specialization of Macdonald's (q, t)-Littlewood–Richardson coefficients that can be expressed alternatively in terms of the refined Verlinde formula. This reveals that the genus zero su ^ (n) m Wess–Zumino–Witten fusion coefficients can be retrieved directly from the (q, t)-Littlewood–Richardson coefficients through the parameter degeneration (q , t) = exp ( 2 π i n c + m ) , exp ( 2 π i c n c + m ) , c → 1 . The refinement thus establishes that at the level of the structure constants (q, t)-deformation provides a vehicle for performing the reduction modulo the fusion ideal via parameter specialization.
- Subjects
CONFORMAL field theory; GROBNER bases; POLYNOMIALS; ALGEBRAIC field theory
- Publication
Communications in Mathematical Physics, 2023, Vol 397, Issue 3, p967
- ISSN
0010-3616
- Publication type
Article
- DOI
10.1007/s00220-022-04506-7