TY - JOUR
T1 - Free filtrations of affine Weyl arrangements and the ideal-Shi arrangements
AU - Abe, Takuro
AU - Terao, Hiroaki
N1 - Funding Information:
The first author is partially supported by JSPS Grants-in-Aid for Young Scientists (B) No. 24740012. The second author is partially supported by JSPS Grants-in-Aid for Scientific Research (A) No. 24244001.
Publisher Copyright:
© 2015, Springer Science+Business Media New York.
PY - 2016/2/1
Y1 - 2016/2/1
N2 - In this article, we prove that the ideal-Shi arrangements are free central arrangements of hyperplanes satisfying the dual partition formula. Then, it immediately follows that there exists a saturated free filtration of the cone of any affine Weyl arrangement such that each subarrangement of the filtration satisfies the dual partition formula. This generalizes the main result in Abe et al. (J. Eur. Math. Soc., to appear) which affirmatively settled a conjecture by Sommers and Tymoczko (Trans. Am. Math. Soc. 358:3493–3509, 2006).
AB - In this article, we prove that the ideal-Shi arrangements are free central arrangements of hyperplanes satisfying the dual partition formula. Then, it immediately follows that there exists a saturated free filtration of the cone of any affine Weyl arrangement such that each subarrangement of the filtration satisfies the dual partition formula. This generalizes the main result in Abe et al. (J. Eur. Math. Soc., to appear) which affirmatively settled a conjecture by Sommers and Tymoczko (Trans. Am. Math. Soc. 358:3493–3509, 2006).
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U2 - 10.1007/s10801-015-0624-z
DO - 10.1007/s10801-015-0624-z
M3 - Article
AN - SCOPUS:84953357248
SN - 0925-9899
VL - 43
SP - 33
EP - 44
JO - Journal of Algebraic Combinatorics
JF - Journal of Algebraic Combinatorics
IS - 1
ER -