  New mathematical objects called Finslerian N-spinors are discussed. The
Finslerian N-spinor algebra is developed. It is found that Finslerian N-spinors
are associated with an N^2-dimensional flat Finslerian space. A generalization
of the epimorphism SL(2,C) --> SO^\uparrow(1,3) to a case of the group SL(N,C)
is constructed.
