We find a new representation of the simple Lie algebra of type E (6) on the polynomial algebra in 16 variables, which gives a fractional representation of the corresponding Lie group on 16-dimensional space. Using this representation and Shen's idea of mixed product, we construct a new functor from D (5)-Mod to E (6)-Mod. A condition for the functor to map a finite-dimensional irreducible D (5)-module to an infinite-dimensional irreducible E (6)-module is obtained. Our results yield explicit constructions of certain infinite-dimensional irreducible weight E6-modules with finite-dimensional weight subspaces. In our approach, the idea of Kostant's characteristic identities plays a key role.
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