  Polynomials with values in an irreducible module of the symmetric group can
be given the structure of a module for the rational Cherednik algebra, called a
standard module. This algebra has one free parameter and is generated by
differential-difference ("Dunkl") operators, multiplication by coordinate
functions and the group algebra. By specializing Griffeth's (arXiv:0707.0251)
results for the G(r,p,n) setting, one obtains norm formulae for symmetric and
antisymmetric polynomials in the standard module. Such polynomials of minimum
degree have norms which involve hook-lengths and generalize the norm of the
alternating polynomial.
