Cubic metaplectic forms on exceptional Lie group of type \(G_ 2\) (Q1900597)

The paper examines cubic metaplectic forms defined on the simple complex Lie group of \(G\)-type realized as the subgroup \(G_2 (\mathbb{C})\) in \(\text{SL} (7, \mathbb{C})\). The Fourier coefficients of the Eisenstein series are computed. Then the Eisenstein series associated with Kubota-Patterson's cubic theta function and its residue at the ``major'' pole are considered. The techniques used for the computations are based on the consideration of the embeddings of \(\text{SL} (2, \mathbb{C})\) into \(G_2 (\mathbb{C})\).