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Zbl 0586.33011
Milne, S.C.
An elementary proof of the Macdonald identities for $A_{\ell}^{(1)}$. (English)
[J] Adv. Math. 57, 34-70 (1985). ISSN 0001-8708

It is shown that the Macdonald identities for $A\sb{\ell}\sp{(1)}$ are a natural consequence of the recent multivariable generalization of classical basic hypergeometric series known as basic hypergeometric series in $U(n)$. More precisely, a $U(n)$ multiple series generalization of the q-binomial theorem is derived and used to generalize Cauchy's elegant proof of Jacobi's triple product identity and to give a direct, elementary proof of the Macdonald identities for $A\sb{\ell}\sp{(1)}$.

MSC 2000:: *33D80 Connections with groups, algebras and related topics
33D15 Basic hypergeometric functions of one variable

Keywords: Macdonald identities; classical basic hypergeometric series; basic hypergeometric series in U(n)

Cited in: Zbl 1148.33015 Zbl 0594.33008

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