Schur functor

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In mathematics, especially in the field of representation theory, Schur functors (named after Issai Schur) are certain functors from the category of modules over a fixed commutative ring to itself. They generalize the constructions of exterior powers and symmetric powers of a vector space. Schur functors are indexed by Young diagrams in such a way that the horizontal diagram with n cells corresponds to the nth symmetric power functor, and the vertical diagram with n cells corresponds to the nth exterior power functor. If a vector space V is a representation of a group G, then ${\displaystyle \mathbb {S} ^{\lambda }V}$ also has a natural action of G for any Schur functor ${\displaystyle \mathbb {S} ^{\lambda }(-)}$.