WHEN: 07.05.15 at 14:15
WHERE: Seminar Room, Arnimallee 2, FU Berlin

Speaker: Torsten Hoge (Leibniz Universität Hannover)

The freeness of ideal subarrangements of Weyl arrangements

The talk is based on joint work with Takuro Abe, Mohamed Barakat,
Michael Cuntz and Hiroaki Terao on Weyl arrangements.

A Weyl arrangement is the arrangement defined by the root system of a
finite Weyl group. When a set of positive roots is an ideal in the root
poset, we call the corresponding arrangement an ideal subarrangement.
Our main theorem asserts that any ideal subarrangement is a free
arrangement and that its exponents are given by the dual partition of
the height distribution, which was conjectured by Sommers-Tymoczko. In
particular, when an ideal subarrangement is equal to the entire Weyl
arrangement, our main theorem yields the celebrated formula by Shapiro,
Steinberg, Kostant, and Macdonald. Our proof of the main theorem heavily
depends on the theory of free arrangements and thus greatly differs from
the earlier proofs of the formula.