Cyclotomic discriminantal arrangements and diagram automorphisms of Lie algebras

Varchenko, Alexander; Young, Charles

doi:10.1093/imrn/rnx225

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学術論文

Cyclotomic discriminantal arrangements and diagram automorphisms of Lie algebras

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Varchenko, Alexander
Max Planck Institute for Mathematics, Max Planck Society;

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https://doi.org/10.1093/imrn/rnx225
(出版社版)

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Varchenko-Young_Cyclotomic discriminantal arrangements and diagram automorphisms of Lie algebras_oa_2019.pdf
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引用

Varchenko, A., & Young, C. (2019). Cyclotomic discriminantal arrangements and diagram automorphisms of Lie algebras. International Mathematics Research Notices, 2019(11), 3376-3458. doi:10.1093/imrn/rnx225.

引用: https://hdl.handle.net/21.11116/0000-0004-41BC-F

要旨

We identify a class of affine hyperplane arrangements that we call cyclotomic discriminantal arrangements. We establish correspondences between the flag and Aomoto
complexes of such arrangements and chain complexes for nilpotent subalgebras of Kac–
Moody type Lie algebras with diagram automorphisms. As part of this construction,
we find that flag complexes naturally give rise to a certain cocycle on the fixed-point
subalgebras of such diagram automorphisms.
As a byproduct, we show that the Bethe vectors of cyclotomic Gaudin models associated to diagram automorphisms are nonzero. We also obtain the Poincare polynomial for the cyclotomic discriminantal arrangements.