The Foulkes-Howe map is the canonical equivariant linear transformation comparing two orders
of iterated symmetric powers. For positive
integers 
and a finite-dimensional complex
vector space 
, one direction convention is
 |
It is obtained by embedding into the iterated vector space tensor product 
using symmetrization, exchanging the rows and
columns of the rectangular array of factors, and projecting onto the target symmetric
powers. It is equivariant for the natural
general linear group action. The direction
convention is part of the notation.
