This has come up several times before:
Definition of the symmetric algebra in arbitrary characteristic for graded vector spacesDefinition of the symmetric algebra in arbitrary characteristic for graded vector spaces
Is there a notation for the symmetric / antisymmetric subspaces of a tensor power that distinguishes them from the symmetric / exterior power?Is there a notation for the symmetric / antisymmetric subspaces of a tensor power that distinguishes them from the symmetric / exterior power?
Symmetric powers and duals of vector bundles in char pSymmetric powers and duals of vector bundles in char p
Is $Sym^n (V^*) \cong Sym^n (V)^\ast$ naturally in positive characteristic?Is $Sym^n (V^*) \cong Sym^n (V)^\ast$ naturally in positive characteristic?
