Geodesic
Invariant subrings of the induced ring on the $4\times4$ symplectic group
Sbornik. Mathematics, Tome 18 (1972) no. 2, pp. 228-234 Cet article a éte moissonné depuis la source Math-Net.Ru

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It is proved that if $\Omega$ is an invariant subring of the induced ring $\operatorname{Ind}_{\mathrm{Sp}_4}^{\varphi,P}(K)$ with ring of values $A$ and maximal induced subring $\operatorname{Ind}_{\mathrm{Sp}_4}^{\varphi,P}(K)$, then $$ 0\to\Omega/\operatorname{Ind}_{\mathrm{Sp}_4}^{\varphi,P}(I)\to\operatorname{Ind}_{GL_2}^{\varphi,B}(A/I) \quad\text{and}\quad 0\to A/I\to\operatorname{Ind}_{GL_2}^{\varphi,B}(A/\mathscr F), $$ and the ideals $~I$ and $\mathscr F$ of $A$ are described. Bibliography: 2 titles. 
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     title = {Invariant subrings of the induced ring on the $4\times4$ symplectic group},
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B. Kh. Kirshtein. Invariant subrings of the induced ring on the $4\times4$ symplectic group. Sbornik. Mathematics, Tome 18 (1972) no. 2, pp. 228-234. http://geodesic.mathdoc.fr/item/SM_1972_18_2_a4/

[1] I. I. Pyatetskii–Shapiro, “Indutsirovannye koltsa i reduktsiya polei abelevykh modulyarnykh funktsii”, Izv. AN SSSR, seriya matem., 34 (1970), 532–546

[2] B. X. Kirshtein, I. I. Pyatetskii–Shapiro, “Invariantnye podkoltsa indutsirovannykh kolets”, Izv. AN SSSR, seriya matem., 34 (1970), 83–89