An upper bound on separable index of certain SL(3)-modules

Let X 3 be the set of all 3 × 3 matrices with non-negative integer entries whose column sum is fixed. We find an upper bound on the set which will turn out to be the maximum of S whenever it is prime. Using this and the Standard Monomial Theory, we get an upper bound of the separable index of certain highest weight representations of SL(3) which is sharper than the one given in V. Balaji & A.J. Parameswaran [Semistable principal bundles-II (positive characteristic), Transform. Groups, 8, (2003), pp. 3–36].