An assembly for a turbomachine turbine includes a housing (1) extending circumferentially about an axis X, sectors (2) intended to form a ring capable of delimiting a gas flow path, each sector (2) comprising a first side (17) and a second side (18) extending radially and circumferentially about the said axis X and spaced axially from each other, each side (17, 18) of the sector (2) including at least one radial bearing surface of an oblong hole capable of cooperating with support pins (13, 14) of the housing (1), at least one of the sides (17, 18) including means (23) for the circumferential positioning of the sector (2) with respect to the housing (1), wherein each radial bearing surface is cylindrical relative to axis X and is capable of bearing on a complementary cylindrical surface relative to axis X of a support pin.