  In this paper we produce further specification of the geometric and algebraic
properties of the earlier introduced superdimensional dual-covariant field
theory (SFT) in a N-dimensional manifold [1] as an approach to a unified field
theory (UFT). Considerations in the present paper are directed by a requirement
of transformational invariance of connections of derivatives of dual state
vector (DSV) and unified gauge field (UGF matrices) to these objects themselves
established by mean of N split metric matrices of a rank {\mu} (SM, an extended
analog of Dirac matrices) in frame of the related Euler-Lagrange equations for
DSV, UGF and SM derived in [1]. This requirement is posed on SFT as one of the
aspects of the general demand of irreducibility claimed to UFT; it leads to
rotational invariance of SM and grand metric tensor (GM) as being structured on
SM. Study in this work has led to explication of geometrical nature of SM and
DSV as spin-affinors (variable in space of the unified manifold) and dual
spin-field, respectively, in accordance with the E. Cartan's theory of spinors
[2, 3, 4].
