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@article{67c048c260d541a3b495d12c557fef54,
title = "Cyclotomic discriminantal arrangements and diagram automorphisms of Lie algebras",
abstract = "Recently a new class of quantum integrable models, the cyclotomic Gaudin models, were described in arXiv:1409.6937, arXiv:1410.7664. Motivated by these, 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 a byproduct, we show that the Bethe vectors of cyclotomic Gaudin models associated to diagram automorphisms are nonzero.",
keywords = "math.QA",
author = "Alexander Varchenko and Young, {Charles A. S.}",
note = "This is a pre-copyedited, author-produced version of an article accepted for publication in International Mathematical Research Notices following peer review. Under embargo. Embargo end date: 25 September 2018. The version of record is available online at: https://doi.org/10.1093/imrn/rnx225.",
year = "2017",
month = sep,
day = "25",
doi = "10.1093/imrn/rnx225",
language = "English",
journal = "International Mathematical Research Notices",
issn = "1073-7928",
publisher = "Oxford University Press",

}

RIS

TY - JOUR

T1 - Cyclotomic discriminantal arrangements and diagram automorphisms of Lie algebras

AU - Varchenko, Alexander

AU - Young, Charles A. S.

N1 - This is a pre-copyedited, author-produced version of an article accepted for publication in International Mathematical Research Notices following peer review. Under embargo. Embargo end date: 25 September 2018. The version of record is available online at: https://doi.org/10.1093/imrn/rnx225.

PY - 2017/9/25

Y1 - 2017/9/25

N2 - Recently a new class of quantum integrable models, the cyclotomic Gaudin models, were described in arXiv:1409.6937, arXiv:1410.7664. Motivated by these, 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 a byproduct, we show that the Bethe vectors of cyclotomic Gaudin models associated to diagram automorphisms are nonzero.

AB - Recently a new class of quantum integrable models, the cyclotomic Gaudin models, were described in arXiv:1409.6937, arXiv:1410.7664. Motivated by these, 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 a byproduct, we show that the Bethe vectors of cyclotomic Gaudin models associated to diagram automorphisms are nonzero.

KW - math.QA

UR - https://doi.org/10.1093/imrn/rnx225

U2 - 10.1093/imrn/rnx225

DO - 10.1093/imrn/rnx225

M3 - Article

JO - International Mathematical Research Notices

JF - International Mathematical Research Notices

SN - 1073-7928

M1 - rnx225

ER -