The quasiinvariants of the symmetric group

Jason Bandlow, Gregg Musiker

Research output: Chapter in Book/Report/Conference proceedingConference contribution

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 languageEnglish (US)
Title of host publicationFPSAC'08 - 20th International Conference on Formal Power Series and Algebraic Combinatorics
Pages599-610
Number of pages12
StatePublished - Dec 1 2008
Event20th International Conference on Formal Power Series and Algebraic Combinatorics, FPSAC'08 - Valparaiso, Chile
Duration: Jun 23 2008Jun 27 2008

Other

Other20th International Conference on Formal Power Series and Algebraic Combinatorics, FPSAC'08
CountryChile
CityValparaiso
Period6/23/086/27/08

Keywords

  • Invariants
  • Quasiinvariants
  • Symmetric group

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