Multiplicative products of Dedekind \(\eta\)-functions and group representations (Q1886127)

The present paper continues the author's investigations of metacyclic groups which began in the papers [1,2]. The author gives all metacyclic groups \(\langle a,b:a^m=e,b^s=e,b^{-1}ab=a^r\rangle\), where \(m=10,14,15,20,21,22\), such that the cusp forms associated with all elements of these groups by an exact representation are multiplicative \(\eta\)-products. She also considers the correspondence between multiplicative \(\eta\)-products and elements of finite order in SL\((5, \mathbb{C})\) by the adjoint representation.