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  Cyclotomic discriminantal arrangements and diagram automorphisms of Lie algebras

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.

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Item Permalink: https://hdl.handle.net/21.11116/0000-0004-41BC-F Version Permalink: https://hdl.handle.net/21.11116/0000-0004-73DD-2
Genre: Journal Article

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 Creators:
Varchenko, Alexander1, Author           
Young, Charles, Author
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1Max Planck Institute for Mathematics, Max Planck Society, ou_3029201              

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 Abstract: 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.

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Language(s): eng - English
 Dates: 2019
 Publication Status: Issued
 Pages: -
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 Rev. Type: Peer
 Identifiers: eDoc: 743013
DOI: 10.1093/imrn/rnx225
URI: https://doi.org/10.1093/imrn/rnx225
URI: https://arxiv.org/abs/1603.07125
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Title: International Mathematics Research Notices
  Abbreviation : IMRN
Source Genre: Journal
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Publ. Info: Oxford University Press
Pages: - Volume / Issue: 2019 (11) Sequence Number: - Start / End Page: 3376 - 3458 Identifier: -