Identities for the Rogers dilogarithm function connected with simple Lie algebras
type: Item
instance of: scholarly article
title: Identities for the Rogers dilogarithm function connected with simple Lie algebras
zbMATH Open document ID: 0685.33014
DOI: 10.1007/BF01840426
published in: Journal of Soviet Mathematics
publication date: 1987-01-01T00:00:00Z
review text: The function \(L(x)=-\int^{x}_{0}[\frac{\log (1-x)}{x}+\frac{\log x}{1-x}]dx\), where \(0\leq x\leq 1\), is called Rogers dilogarithmic function. Let G be a simple Lie algebra of rank \(\ell\), g the dual Coxeter number and \(\phi =\pi /(r+g)\). The author conjectures that \[ \sum^{\ell}_{k=0}\sum^{r}_{m=1}L(f_ m^{(k)}(\phi))=(r \dim G/(r+g)\quad)(\pi^ 2/6). \] It is proved this formula for the Lie algebra \(A_ n\) and for classical Lie algebras of rank \(\ell\), whre \(\ell \leq 4\).
Mathematics Subject Classification ID: 33C80
Mathematics Subject Classification ID: 22E70
Mathematics Subject Classification ID: 68W30
zbMATH DE Number: 4122340
zbMATH Keywords: Clebsch-Gordan coefficient
zbMATH Keywords: Racah coefficient
zbMATH Keywords: dilogarithmic
zbMATH Keywords: Rogers function
zbMATH Keywords: semi-simple Lie algebra
zbMATH Keywords: Coxeter number
author: Anatol N. Kirillov
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4122340