 The universal "R"-module formula_11 that extends formula_4 to a mapping of "R"-modules formula_13 is the image of "E" under the Schur functor indexed by λ.For an example of the condition (3) placed on formula_4
suppose that λ is the partition formula_15 and the tableau
"T" is numbered such that its entries are 1, 2, 3, 4, 5 when read
top-to-bottom (left-to-right).Taking formula_16 (i.e.,
the numbers in the second column of "T") we have

while if formula_18 then

Fix a vector space "V" over a field of characteristic zero.