Borwein identity and vertex operator algebras (Q1587662)

Let \(V= \sum V_n\) be a vertex operator algebra and \(\tau\) and \(\sigma\) a pair of two conjugate automorphisms of \(V\). In the paper under review the authors note that the following \(q\)-character identity holds: \[ \sum \text{tr} ( \tau |_{V_n}) q^{n}= \sum\text{tr} (\sigma|_{V_n}) q^{n}. \] They apply this general identity on certain vertex operator algebras associated to root lattices. As a consequence, they prove the Borwein identity [\textit{J. M. Borwein} and \textit{P. B. Borwein}, Trans. Am. Math. Soc. 323, No. 2, 691-701 (1991; Zbl 0725.33014)] and the classical Jacobi identity.