The group $G_2(\mathbb{C})$ in connection with the theory of metaplectic forms
Zapiski Nauchnykh Seminarov POMI, Automorphic functions and number theory. Part III, Tome 162 (1987), pp. 169-185

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Some preliminary information which makes the consideration of metaplectic forms on $G_2(\mathbb{C})$ possible is recounted.
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     title = {The group $G_2(\mathbb{C})$ in connection with the theory of metaplectic forms},
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N. V. Proskurin. The group $G_2(\mathbb{C})$ in connection with the theory of metaplectic forms. Zapiski Nauchnykh Seminarov POMI, Automorphic functions and number theory. Part III, Tome 162 (1987), pp. 169-185. http://geodesic.mathdoc.fr/item/ZNSL_1987_162_a5/