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Algebras and Representation Theory

, Volume 14, Issue 4, pp 625–638 | Cite as

Strong Lefschetz Elements of the Coinvariant Rings of Finite Coxeter Groups

  • Toshiaki Maeno
  • Yasuhide Numata
  • Akihito WachiEmail author
Article

Abstract

For the coinvariant rings of finite Coxeter groups of types other than H4, we show that a homogeneous element of degree one is a strong Lefschetz element if and only if it is not fixed by any reflections. We also give the necessary and sufficient condition for strong Lefschetz elements in the invariant subrings of the coinvariant rings of Weyl groups.

Keywords

Coxeter group Weyl group Coinvariant ring Strong Lefschetz property Flag variety Hard Lefschetz theorem 

Mathematics Subject Classifications (2010)

Primary—20F55; Secondary—13A50 14M15 14N15 

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Copyright information

© Springer Science+Business Media B.V. 2010

Authors and Affiliations

  • Toshiaki Maeno
    • 1
  • Yasuhide Numata
    • 2
    • 3
  • Akihito Wachi
    • 4
    Email author
  1. 1.Department of Electrical EngineeringKyoto UniversityKyotoJapan
  2. 2.Department of Mathematical InformaticsThe University of TokyoTokyoJapan
  3. 3.Japan Science and Technology Agency (JST), CRESTTokyoJapan
  4. 4.Department of MathematicsHokkaido University of EducationKushiroJapan

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