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math.AG2025
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…
math.RT2025
Cactus flower spaces and monodromy of Bethe vectors
Joel Kamnitzer, Leonid Rybnikov
We continue the study of cactus flower moduli spaces and Gaudin models started in arXiv:2308.06880, arXiv:2407.06424. We show that isomorphism classes of operadic…
math.CO2025
Maximal transitivity of the cactus group on standard Young tableaux
Sophia Liao, Leonid Rybnikov
The action of the cactus group on Young tableaux of a given shape goes back to Berenstein and Kirillov and arises naturally in the study of crystal bases and quantum inte…