Mathematics – Combinatorics
Scientific paper
2010-09-13
SIGMA 7 (2011), 026, 48 pages
Mathematics
Combinatorics
Scientific paper
10.3842/SIGMA.2011.026
Vector-valued Jack polynomials associated to the symmetric group ${\mathfrak S}_N$ are polynomials with multiplicities in an irreducible module of ${\mathfrak S}_N$ and which are simultaneous eigenfunctions of the Cherednik-Dunkl operators with some additional properties concerning the leading monomial. These polynomials were introduced by Griffeth in the general setting of the complex reflections groups $G(r,p,N)$ and studied by one of the authors (C. Dunkl) in the specialization $r=p=1$ (i.e. for the symmetric group). By adapting a construction due to Lascoux, we describe an algorithm allowing us to compute explicitly the Jack polynomials following a Yang-Baxter graph. We recover some properties already studied by C. Dunkl and restate them in terms of graphs together with additional new results. In particular, we investigate normalization, symmetrization and antisymmetrization, polynomials with minimal degree, restriction etc. We give also a shifted version of the construction and we discuss vanishing properties of the associated polynomials.
Dunkl Charles F.
Luque Jean-Gabriel
No associations
LandOfFree
Vector-Valued Jack Polynomials from Scratch does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Vector-Valued Jack Polynomials from Scratch, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Vector-Valued Jack Polynomials from Scratch will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-337572