The polarized low-temperature absorption spectra of the 3d(1) ion MnO42- in the Cs2SO4 host consist of a very weak, highly-structured band in the near-infrared (NIR) region corresponding to the (2)E-->T-2(2)(d-->d) transition and a series of intense ligand-to-metal charge transfer (LMCT) excitations above 16 000 cm(-1). As a result of the low-symmetry crystal-field (CF) potential in Cs2SO4 the T-2(2) ligand-field (LF) state of MnO42- is split into its three orbital components at 10 557, 10 848, and 10 858 cm(-1) above the ground state. The lowest-energy component serves as initial state for broadband luminescence to the (2)E ground state, exhibiting unusually well-resolved fine structure at 15 K. The orbital splitting of (2)E is 969 cm(-1) and thus larger by more than 1 order of magnitude and of opposite sign compared to the result of a ligand-field calculation within the angular-overlap model (AOM). This discrepancy is explained with the large contribution of the second-nearest neighbor Cs+ ions to the CF potential of MnO42- in the Cs2SO4 host lattice. The vibrational progressions in the (2)Et<->T-2(2) absorption and luminescence spectra are dominated by O-Mn-O bending modes. This is the result of a weak Exe and a stronger T(2)xe Jahn-Teller (JT) effect in the ground and excited LF states, respectively. The observed vibronic levels in the luminescence spectrum are fitted with a single-mode Exe JT Hamiltonian with an additional term representing the noncubic CF potential, in Cs2SO4. The JT effect in the T-2(2) LF state causes a large displacement of the emitting level along the two coordinates of the e mode and thus substantially. affects the intensity distribution in the luminescence spectrum. The fitted linear and quadratic vibronic constants for the (2)E ground state are 91 and 12 cm(-1), respectively, and for the T-2(2) excited state the Linear coupling constant is -790 cm(-1). The corresponding JT stabilization energies are 14 and 925 cm(-1) for (2)E and T-2(2), respectively.