Crystals and monodromy of Bethe vectors

DOI10.1215/00127094-2020-0003zbMath1468.17013arXiv1708.05105OpenAlexW2748601755MaRDI QIDQ2217882

Iva Halacheva, Leonid Rybnikov, Joel Kamnitzer, Alex Weekes

Publication date: 12 January 2021

Published in: Duke Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1708.05105

zbMATH Keywords

representation theorycrystalsBethe vectorsGaudin algebrascactus group

Mathematics Subject Classification ID

Representations of Lie algebras and Lie superalgebras, algebraic theory (weights) (17B10) Applications of Lie algebras and superalgebras to integrable systems (17B80)

Related Items (13)

Simplicity of spectra for Bethe subalgebras in \(\mathrm{Y}(\mathfrak{gl}_2)\) ⋮ Gaudin algebras, RSK and Calogero–Moser cells in Type A ⋮ Shift of argument algebras and de Concini–Procesi spaces ⋮ On Schützenberger modules of the cactus group ⋮ Automorphisms of finite order, periodic contractions, and Poisson-commutative subalgebras of \({\mathcal{S}}(\mathfrak{g})\) ⋮ Categorical braid group actions and cactus groups ⋮ Enveloping algebras and geometric representation theory. Abstracts from the workshop held October 31 -- November 6, 2021 (hybrid meeting) ⋮ An action of the cactus group on shifted tableau crystals ⋮ A topological proof of the Shapiro-Shapiro conjecture ⋮ Gelfand-Tsetlin degeneration of shift of argument subalgebras in types B, C and D ⋮ Combinatorial wall-crossing and the Mullineux involution ⋮ Quantisation and nilpotent limits of Mishchenko–Fomenko subalgebras ⋮ Spectra of Bethe subalgebras of \(Y(\mathfrak{gl}_n)\) in tame representations

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