# Darstellungstheorietage and Nikolaus Conference 2013

Speaker: Nils Amend (Bochum)

Title: Supersolvable Restrictions of Reflection Arrangements

Abstract: Let $$A = (A, V)$$ be a complex hyperplane arrangement and let $$L(A)$$ denote its intersection lattice. The arrangement $$A$$ is called supersolvable, provided its lattice $$L(A)$$ is supersolvable. For $$X$$ in $$L(A)$$, it is known that the restriction of $$A$$ to $$X$$ is supersolvable provided $$A$$ is.

Suppose that $$W$$ is a finite, unitary reflection group acting on the complex vector space $$V$$. Let $$A = (A(W), V)$$ be its associated hyperplane arrangement. Hoge and Röhrle classified all supersolvable reflection arrangements. Extending this work, we classify all supersolvable restrictions of reflection arrangements to elements in $$L(A)$$.

We will discuss this classification with particular respect to the infinite families of irreducible complex reflection groups. This is a report on joint work with Hoge and Röhrle.