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)
type: Item
instance of: scholarly article
title: 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)
zbMATH Open document ID: 0596.17009
author: Erhard Neher
published in: Jahresbericht der Deutschen Mathematiker-Vereinigung (DMV)
publication date: 1985-01-01T00:00:00Z
review text: 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 [\textit{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.
Mathematics Subject Classification ID: 17B65
Mathematics Subject Classification ID: 11F11
Mathematics Subject Classification ID: 05A19
Mathematics Subject Classification ID: 11P81
zbMATH DE Number: 3959721
zbMATH Keywords: Euler's pentagonal number theorem
zbMATH Keywords: Jacobi's triple product identity
zbMATH Keywords: Dedekind's \(\eta \) -function
zbMATH Keywords: root system
zbMATH Keywords: affine Lie algebras
zbMATH Keywords: Macdonald's \(\eta \) -identities
zbMATH Keywords: bibliography
reviewed by: Günter Köhler
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 3959721