Invariant subrings of induced rings
Sbornik. Mathematics, Tome 16 (1972) no. 3, pp. 381-388
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Let $\Phi(G_{k_\mathfrak p},P_{\Theta,k_\mathfrak p},\varphi,K)$ be the ring induced by the homorphism $\varphi\colon P_{\Theta,k_\mathfrak p}\to \operatorname{Aut}K$, where $G_{k_\mathfrak p}$ is the Chevalley group over the field $k_\mathfrak p$ of $\mathfrak p$-adic numbers and $P_{\Theta,k_\mathfrak p}$ is a parabolic sybgroup. In this note we characterize a class of subrings of this ring which are invariant relative to translations by elements of the group $G_{k_\mathfrak p}$. Bibliography: 4 titles.
[1] K. Shevalle, “O nekotorykh prostykh gruppakh”, Matematika, 2:1 (1958), 3–35 | MR
[2] A. Borel, Zh. Tits, “Reduktivnye gruppy”, Matematika, 11:1 (1967), 43–112
[3] I. I. Pyatetskii–Shapiro, “Indutsirovannye koltsa i reduktsiya polei abelevykh modulyarnykh funktsii”, Izv. AN SSSR, seriya matem., 34 (1970), 532–646
[4] B. X. Kirshtein, I. I. Pyatetskii–Shapiro, “Invariantnye podkoltsa indutsirovannykh kolets”, Izv. AN SSSR, seriya matem., 34 (1970), 83–89