On quasiinvariants of $S_n$ of hook shape

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Tsuchida, Tadayoshi
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Abstract
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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.
Comment: 28 pages
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Mathematics - Combinatorics, 68R05, 05E10
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