Explicit Universal Proof of ≠ —Communicated with S.A.Chin—

Let be any -type Lie algebra with l ≥ 2 over an algebraically closed field F of characteristic 5. Let V be an irreducible L-module corresponding to some points and let p : () ⇾ (V) be its corresponding representation. In this paper, in order to prove that the equality about the versus problem out of the 7 Clay problems [Ja] [KSPY] does not hold, the Kernel = of ρ and the coset of ≅ (V) will be investigated. Furthermore, given a particular element of (), we consider the expression formulae of x in the cosets of ()/. The expression gives rise to a nonhomogeneous system of linear equations, and this system has an algorithm by the Cramer's formula. We consider a counting problem asking whether a given particular element x of belongs to a coset of the form (see Theorem 5.1) and how many coefficients are there in e ∈ m modulo having their absolute values equal to ()