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- W3124366717 abstract "We study degenerations of Bethe subalgebras B(C) in the Yangian $$Y(mathfrak {gl}_n)$$ , where C is a regular diagonal matrix. We show that closure of the parameter space of the family of Bethe subalgebras, which parameterizes all possible degenerations, is the Deligne–Mumford moduli space of stable rational curves $$overline{M_{0,n+2}}$$ . All subalgebras corresponding to the points of $$overline{M_{0,n+2}}$$ are free and maximal commutative. We describe explicitly the “simplest” degenerations and show that every degeneration is the composition of the simplest ones. The Deligne–Mumford space $$overline{M_{0,n+2}}$$ generalizes to other root systems as some De Concini–Procesi resolution of some toric variety. We state a conjecture generalizing our results to Bethe subalgebras in the Yangian of arbitrary simple Lie algebra in terms of this De Concini–Procesi resolution." @default.
- W3124366717 created "2021-02-01" @default.
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- W3124366717 date "2017-12-01" @default.
- W3124366717 modified "2023-09-25" @default.
- W3124366717 title "Degeneration of Bethe subalgebras in the Yangian of $$mathfrak {gl}_n$$ gl n" @default.
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- W3124366717 doi "https://doi.org/10.1007/s11005-017-1031-2" @default.
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