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Jacobis Tripelprodukt-Identität und $$\eta$$-Identitäten in der Theorie affiner Lie-Algebren. (Jacobi’s triple product identity and $$\eta$$- identities in the theory of affine Lie algebras). (German) Zbl 0596.17009
This is a nicely readable written version of the author’s inaugural lecture. It begins with a report on classical results in partition theory: Euler’s pentagonal number theorem, Jacobi’s triple product identity, and identities for the first and third power of Dedekind’s $$\eta$$-function. Then the author explains the transcription of Jacobi’s triple product identity into a formula on the root system and the Weyl group of the affine Lie algebra attached to sl(2,$${\mathbb{C}})$$. Finally he discusses the generalization to other affine Lie algebras which yield Macdonald’s $$\eta$$-identities [I. G. Macdonald, Invent. Math. 15, 91-143 (1972; Zbl 0244.17005)], exemplified by $$\eta^{24}$$ and $$\eta^{248}$$. There is a bibliography of 61 items.
Reviewer: G.Köhler

##### MSC:
 17B65 Infinite-dimensional Lie (super)algebras 11F11 Holomorphic modular forms of integral weight 05A19 Combinatorial identities, bijective combinatorics 11P81 Elementary theory of partitions