Spinor representation of Lie algebra for complete linear group
  Spinor representation of group GL(4,R) on special spinor space is developed. Representation space has a structure of the fiber space with the space of diagonal metricses as the base and standard spinor space as typical fiber.   Non-isometric motions of the space-time entail spinor transformations which are represented by translation over fibering base in addition to standard $Spin(4,C)$ representation. 
C.V. Usenko and B.I. Lev