Geodesic
Invariant subrings of the induced ring on the $4\times4$ symplectic group
Sbornik. Mathematics, Tome 18 (1972) no. 2, pp. 228-234

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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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     author = {B. Kh. Kirshtein},
     title = {Invariant subrings of the induced ring on the $4\times4$ symplectic group},
     journal = {Sbornik. Mathematics},
     pages = {228--234},
     publisher = {mathdoc},
     volume = {18},
     number = {2},
     year = {1972},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1972_18_2_a4/}
}
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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/