Séminaire Lotharingien de Combinatoire, B64a (2010), 31 pp.
Charles F. Dunkl
Symmetric and Antisymmetric Vector-valued Jack Polynomials
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
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.
Received: June 7, 2010.
Revised: September 30, 2010.
Accepted: September 30, 2010.
The following versions are available: