Schur functors are functors from the category of vector spaces to itself. If we take an operator $M: V->V$ and apply a Schur functor to it and then calculate trace $Tr(M^{\Lambda})$ we will get Schur polynomial in the eigenvalues of $M$.

**Question** Can one generalize (deform) Schur functors, such that
$Tr(M^{\Lambda})$ will give polynomials which generalize (deform) Schur polynomials e.g.
Hall-Littlewood polynomial, or Jack polynomial and most generally
Macdonald polynomials ?