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## Degeneration of Bethe subalgebras in the Yangian of $gl_n$

Series math "arxiv.org". arXiv:1703.04147. Cornell University, 2017
We study degenerations of Bethe subalgebras $B(C)$ in the Yangian $Y(\fgl_n)$, where $C$ is a regular diagonal matrix. We show that closure of the parameter space of the family of Bethe subalgebras is the Deligne-Mumford moduli space of stable rational curves $\overline{M_{0,n+2}}$ and state a conjecture generalizing this result to Bethe subalgebras in Yangians of arbitrary simple Lie algebra. We prove that all subalgebras corresponding to the points of $\overline{M_{0,n+2}}$ are free and maximal commutative. We also describe explicitly the simplest'' degenerations and show that every degeneration is the composition of the simplest ones.