The first polarized low-temperature absorption and luminescence spectra of manganese-doped crystals of BaSO4 containing essentially MnO42- are reported. By using a flux composed of NaCl, KCI, and CsCl we were able to grow BaSO4:Mn6+ crystals below 620 degrees C. This prevents the simultaneous presence of MnO43- besides MnO42-, which was mainly responsible for the erroneous assignments of the absorption spectrum in the literature. In the BaSO4 host the MnO42- ion occupies a site of C-s, symmetry, and the orbital degeneracies of the E and T states are thus lifted. Above 16 000 cm(-1) the absorption spectra consist of a series of intense ligand-to-metal charge transfer (LMCT) excitations. Their marked polarization dependence allows an unambiguous band assignment in the parent T-d symmetry. The three origins of the E-2 --> T-2(2) ligand-field (LF) transition peak at 11 074, 11 570, and 11 790 cm(-1). The lowest-energy component of T-2(2) serves as the initial state for broadband luminescence in the near-infrared (near-IR) region with a maximum at 9300 cm(-1). Below 100 K the quantum yield is unity and the radiative lifetime is 2.75 mu s, and at 300 K the quantum yield is still 20%, In both the E-2 <----> ?T-2(2) (d --> d) absorption and luminescence spectra the vibrational structure is dominated by progressions in O-Mn-O bending modes whereas coupling to the totally symmetric Mn-O stretching mode is less pronounced. The luminescence band shapes for the transitions to the two orbital components of E-2 are strikingly different; the Huang-Rhys parameters for the bending-mode progressions obtained from fits of simulated band shapes to the experimental spectra are 1.3 and 3.7, respectively. This is due to weak Exe and stronger T(2)xe Jahn-Teller (JT) effects in the ground and excited LF states, respectively. The linear vibronic coupling constants are f(E) approximate to 180 cm(-1) and f(T) approximate to -730 cm(-1) and the corresponding JT stabilization energies E-JT(2E) approximate to 50 cm(-1) and E-JT(T-2(2)) approximate to 780 cm(-1) respectively.