The representation of the Hubbard operators in terms of the
spin$-\frac{1}{2}$ operators and the fermion operator with spin$-\frac{1}{2}$
is proposed.
In the low-energy limit this representation is reduced to the representation
following from the Hubbard diagramm technique. In framework of this approach
motion of a hole in an antiferromagnetic state of the t-J model is considered.
It is shown that the primary hole energy is strongly renormalized and the band
width has an order of J rather than t.
The functional integral for the strongly correlated model induced by the
obtained representation is formulated. The representation of the total Hubbard
algebra for states in the lower and the upper Hubbard bands is formulated in
terms of the spin$-\frac{1}{2}$ and two fermion fields with spin$-\frac{1}{2}$
is formulated.