## Abstract

For m a non-negative integer and G a Coxeter group, we denote by QI _{m}(G) the ring of m-quasiinvariants of G, as defined by Chalykh, Feigin, and Veselov. These form a nested series of rings, with QI _{0}(G) the whole polynomial ring, and the limit QI _{∞} (G) the usual ring of invariants. Remarkably, the ring QI _{m}(G) is freely generated over the ideal generated by the invariants of G without constant term, and the quotient is isomorphic to the left regular representation of G. However, even in the case of the symmetric group, no basis for QI _{m}(G) is known. We provide a new description of QI _{m}(S _{n}), and use this to give a basis for the isotypic component of QI _{m}(S _{n}) indexed by the shape [n - 1, 1].

Original language | English (US) |
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Title of host publication | FPSAC'08 - 20th International Conference on Formal Power Series and Algebraic Combinatorics |

Pages | 599-610 |

Number of pages | 12 |

State | Published - Dec 1 2008 |

Event | 20th International Conference on Formal Power Series and Algebraic Combinatorics, FPSAC'08 - Valparaiso, Chile Duration: Jun 23 2008 → Jun 27 2008 |

### Other

Other | 20th International Conference on Formal Power Series and Algebraic Combinatorics, FPSAC'08 |
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Country | Chile |

City | Valparaiso |

Period | 6/23/08 → 6/27/08 |

## Keywords

- Invariants
- Quasiinvariants
- Symmetric group