The Strong Lefschetz Property for Coinvariant Rings of Finite Reflection Groups
نویسنده
چکیده
In this paper we prove that a deformed tensor product of two Lefschetz algebras is a Lefschetz algebra. We then use this result in conjunction with some basic Schubert calculus to prove that the coinvariant ring of a finite reflection, of any type other than H4 or E8, has the strong Lefschetz property.
منابع مشابه
Geometric and Combinatorial Aspects of 1-Skeleta
GEOMETRIC AND COMBINATORIAL ASPECTS OF 1-SKELETA MAY 2010 CHRIS R. MCDANIEL, B.S., UNIVERSITY OF WASHINGTON Ph.D., UNIVERSITY OF MASSACHUSETTS AMHERST Directed by: Professor Tom Braden In this thesis we investigate 1-skeleta and their associated cohomology rings. 1-skeleta arise from the 0and 1-dimensional orbits of a certain class of manifold admitting a compact torus action and many questions...
متن کامل1 M ar 2 00 7 The strong Lefschetz property of the coinvariant ring of the Coxeter group of type
We prove that the coinvariant ring of the irreducible Coxeter group of type H4 has the strong Lefschetz property.
متن کاملExamples That the Strong Lefschetz Property Does Not Survive Symplectic Reduction
In this paper we construct a family of six-dimensional compact non-Kähler Hamiltonian S-manifolds, each of which satisfies the strong Lefschetz property itself but nevertheless has a non-Lefschetz symplectic quotient. This provides the first known counter examples to the question whether the strong Lefschetz property descends to the symplectic quotient. In addition we also show how to vary our ...
متن کاملA Class of Hilbert Series and the Strong Lefschetz Property
We determine the class of Hilbert series H so that if M is a finitely generated zero-dimensional R-graded module with the strong Lefschetz property, then M ⊗k k[y]/(y ) has the strong Lefschetz property for y an indeterminate and all positive integers m if and only if the Hilbert series of M is in H. Given two finite graded R-modules M and N with the strong Lefschetz property, we determine suff...
متن کاملN ov 2 00 8 EXTENDING THE COINVARIANT THEOREMS OF CHEVALLEY , SHEPHARD – TODD , MITCHELL , AND SPRINGER
We extend in several directions invariant theory results of Chevalley, Shephard and Todd, Mitchell and Springer. Their results compare the group algebra for a finite reflection group with its coinvariant algebra, and compare a group representation with its module of relative coinvariants. Our extensions apply to arbitrary finite groups in any characteristic.
متن کامل