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We study an interplay between the orbital degeneracy and spin-orbit couplinggiving rise to spin-orbital entangled states. As a specific example, we analyzethe interaction of electrons occupying triply degenerate single-ion $t_{2g}$levels with trigonal vibronic modes (the $t\otimes T$ problem). A more generalproblem of the electron-lattice interaction involving both tetragonal andtrigonal vibrations is also considered. It is shown that the result of suchinteraction crucially depends on the occupation of $t_{2g}$ levels leading toeither the suppression or enhancement of the Jahn-Teller effect by thespin-orbit coupling.

Interplay of the Jahn--Teller Effect and Spin-Orbit Coupling: The Case of Trigonal Vibronic Modes