Geodesic
Symmetric and Antisymmetric Vector-valued Jack Polynomials
Séminaire lotharingien de combinatoire, Tome 64 (2010-2011)

Voir la notice de l'acte provenant de la source Séminaire Lotharingien de Combinatoire website

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. 

@article{SLC_2010-2011_64_a0,
     author = {Charles F. Dunkl},
     title = {Symmetric and {Antisymmetric} {Vector-valued} {Jack} {Polynomials}},
     journal = {S\'eminaire lotharingien de combinatoire},
     publisher = {mathdoc},
     volume = {64},
     year = {2010-2011},
     url = {http://geodesic.mathdoc.fr/item/SLC_2010-2011_64_a0/}
}
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Charles F. Dunkl. Symmetric and Antisymmetric Vector-valued Jack Polynomials. Séminaire lotharingien de combinatoire, Tome 64 (2010-2011). http://geodesic.mathdoc.fr/item/SLC_2010-2011_64_a0/