On quasiinvariants of $S_{n}$ of hook shape

Abstract

O. Chalykh, A.P. Veselov and M. Feigin introduced the notion of quasiinvariants of Coxeter groups, which is a generalization of invariants. In [2], Bandlow and Musiker showed that for the symmetric group $S_{n}$ of order $n$, the space of quasiinvariants has a decomposition indexed by standard tableaux. They gave a description of a basis for the components indexed by standard tableaux of shape $(n-1,1)$. In this paper, we generalize their results to a description of a basis for the components indexed by standard tableaux of arbitrary hook shape.