On quasiinvariants of $S_n$ of hook shape

Details On quasiinvariants of $S_n$ of hook shape On quasiinvariants of $S_n$ of hook shape

2008-07-11

arxiv.org/abs/0807.1892v1

Mathematics

Combinatorics

28 pages

Scientific paper

Chalykh, Veselov and Feigin introduced the notions of quasiinvariants for 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 basis for the components indexed by standard tableaux of shape $(n-1,1)$. In this paper, we generalize their results to a description of basis for the components indexed by standard tableaux of arbitrary hook shape.

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