9 citations · 10 across the 7 of their papers we have counts for
8 papers
Bethe subspaces and wonderful models for toric arrangements
Aleksei Ilin, Leonid Rybnikov
We study the family of commutative subspaces in the trigonometric holonomy Lie algebra , introduced by Toledano Laredo, for an arbitrary root system . We ca…
Lightweight Safety Guardrails via Synthetic Data and RL-guided Adversarial Training
Aleksei Ilin, Gor Matevosyan, Xueying Ma +5
We introduce a lightweight yet highly effective safety guardrail framework for language models, demonstrating that small-scale language models can achieve, and even surpass, the pe…
Gaudin models and moduli space of flower curves
Aleksei Ilin, Joel Kamnitzer, Leonid Rybnikov
We introduce and study the family of trigonometric Gaudin subalgebras in for arbitrary simple Lie algebra . This is the family of commutative subalgebras of ma…
The moduli space of cactus flower curves and the virtual cactus group
Aleksei Ilin, Joel Kamnitzer, Yu Li +2
The space $ \ft_n = \C^n/\C $ of points on the line modulo translation has a natural compactification $ \overline \ft_n $ as a matroid Schubert variety. In this space, pairwise…
Spectra of Bethe subalgebras of in tame representations
Aleksei Ilin, Inna Mashanova-Golikova, Leonid Rybnikov
We study the eigenproblem for Bethe subalgebras of the Yangian in tame representations, i.e. in finite dimensional representations which admit Gelfand-Tsetlin…
On classical limits of Bethe subalgebras in Yangians
Aleksei Ilin, Leonid Rybnikov
The Yangian of a simple Lie algebra can be regarded as a deformation of two different Hopf algebras: the universal enveloping algebra $U(\mathfrak{…
Bethe subalgebras in Yangians and the wonderful compactification
Aleksei Ilin, Leonid Rybnikov
We study the family of Bethe subalgebras in the Yangian parameterized by the corresponding adjoint Lie group . We describe their classical limits as subalgebra…
Degeneration of Bethe subalgebras in the Yangian of
Aleksei Ilin, Leonid Rybnikov
We study degenerations of Bethe subalgebras in the Yangian , where is a regular diagonal matrix. We show that closure of the parameter space of the f…