Cyclotomic discriminantal arrangements and diagram automorphisms of Lie algebras

Alexander Varchenko, Charles A. S. Young

Research output: Contribution to journalArticlepeer-review

115 Downloads (Pure)

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.
Original languageEnglish
Article numberrnx225
Pages (from-to)3376–3458
Number of pages83
JournalInternational Mathematical Research Notices
Volume2019
Issue number11
Early online date25 Sept 2017
DOIs
Publication statusE-pub ahead of print - 25 Sept 2017

Keywords

  • math.QA

Fingerprint

Dive into the research topics of 'Cyclotomic discriminantal arrangements and diagram automorphisms of Lie algebras'. Together they form a unique fingerprint.

Cite this