The Adjoints of the Schur Functor

Abstract

We show that the left and right adjoint of the Schur functor can be expressed in terms of the monoidal structure of strict polynomial functors. Using this result we give a necessary and sufficient condition for when the tensor product of two simple strict polynomial functors is again simple.

References in corpus (1)

• Highest weight categories and strict polynomial functors

Cited by in corpus (1)

• Relating tensor structures on representations of general linear and symmetric groups