The Structure Of U(Sl(N,F))-module A(N；M)

When the character of F is a prime number p(p≥3),the diVided power algebra (?)((n,F))(p(?)n)is realized as u(sl(n,F))-module.Then we discuss the structure to sub-modules(?)(n；(?))of(?)((n,F)). Because(?)(n；(?))is the direct sum of its submodules (?)(n；(?))s which is (?)(n；(?))’s homogeneous spaces,the u(sf(n,F))-module structures of (?)(n；(?))s are mainly discussed in this paper.First of all,the transformation under the u(sl(n,F))action of F-base elements of.(?)(n；(?))s are discussed.By use of the transfor-mation we find the u(sl(n,F))-generators and Loewy Filtration of(?)(n；(?))s and prove that(?)(n；(?))s is indecomposable module.The rigidity of(?)(n；(?))s is proved by using the Loewy Filtration and u(sl(n,F))-generators of every Loewy layer is found.Finally, a u(sl(n,F))-module filtration of(?)(n；(?))s is got by the relation between the energy de-gree of elements of(?)(n；(?))s and p hexadecimal in which submodules of(?)(n；(?))s and quotient modules have similar u(sl(n,F))-module structures with(?)(n；(?))s.