Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The freeness of ideal subarrangements of 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.

1
The categories of this paper are: cs
6
The categories of this paper are: astro-ph
31
The categories of this paper are: ao-sci
11
The categories of this paper are: hep-lat
3
The categories of this paper are: physics
18
The categories of this paper are: econ
20
The categories of this paper are: acc-phys
26
The categories of this paper are: bayes-an
16
The categories of this paper are: stat
35
The categories of this paper are: mtrl-th
7
The categories of this paper are: hep-th
13
The categories of this paper are: quant-ph
30
The categories of this paper are: q-alg
37
The categories of this paper are: supr-con
12
The categories of this paper are: nucl-th
32
The categories of this paper are: atom-ph