Macdonald identities
In mathematics, the Macdonald identities are some infinite product identities associated to affine root systems, introduced by Ian Macdonald (1972). They include as special cases the Jacobi triple product identity, Watson's quintuple product identity, several identities found by Dyson (1972), and a 10-fold product identity found by Winquist (1969).
Kac (1974) and Moody (1975) pointed out that the Macdonald identities are the analogs of the Weyl denominator formula for affine Kac–Moody algebras and superalgebras.
References
Demazure, Michel (1977), "Identités de Macdonald", Séminaire Bourbaki, 28e année (1975/1976), Exp. No. 483, Lecture Notes in Math 567, Berlin, New York: Springer-Verlag, pp. 191–201, MR 0476815
Dyson, Freeman J. (1972), "Missed opportunities", Bulletin of the American Mathematical Society 78: 635–652, doi:10.1090/S0002-9904-1972-12971-9, ISSN 0002-9904, MR 0522147
Kac, Victor G (1974), "Infinite-dimensional Lie algebras, and the Dedekind η-function", Akademija Nauk SSSR. Funkcionalnyi Analiz i ego Priloženija 8 (1): 77–78, doi:10.1007/BF02028313, ISSN 0374-1990, MR 0374210
