 Let "R" be a commutative ring, "E" an "R"-module
and λ a partition of a positive integer "n".Let "T" be a Young tableau of shape λ, thus indexing the factors of the "n"-fold direct product, "E" × "E" × ... × "E", with the boxes of "T".Consider those maps of "R"-modules formula_3 satisfying the following conditions

(1) formula_4 is multilinear,

(2) formula_4 is alternating in the entries indexed by each column of "T",

(3) formula_4 satisfies an exchange condition stating that if formula_7 are numbers from column "i" of "T" then

where the sum is over "n"-tuples "x' " obtained from "x" by exchanging the elements indexed by "I" with any formula_9 elements indexed by the numbers in column formula_10 (in order).