L. Rybnikov

collaborators

7 papers

math.RT2026

Athinization of irreducible $gl_{n}$ -modules with dominant highest weights

Mikhail Bershtein, Evgeny Mukhin, Leonid Rybnikov +1

We study the Gelfand-Tsetlin realization of generic Verma modules for the affine Lie algebra $gl_{n}$ by viewing them as thin modules over the affine Yangian $Y(…

math.QA2026

$(gl_{n}, gl_{m})$ -duality and Olshanski homomorphism

B. Feigin, L. Rybnikov, F. Uvarov

We show that the images of the Bethe subalgebras of the Yangians $Y (gl_{n})$ and $Y (gl_{m})$ under the homomorphisms to $U (gl_{n + m})$ given by the…

math.RT2026

Bethe subalgebras in antidominantly shifted Yangians

Vasily Krylov, Leonid Rybnikov

The loop group $G ((z^{- 1}))$ of a simple complex Lie group $G$ has a natural Poisson structure. We introduce a natural family of Poisson commutative subalgebras $\overline{\mathbf{…

math.CO2026

Maximal transitivity of the cactus group on standard Young tableaux

Sophia Liao, Leonid Rybnikov

The action of the cactus group $C_{n}$ on Young tableaux of a given shape $I^»$ goes back to Berenstein and Kirillov and arises naturally in the study of crystal bases and quantum int…

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 $t_{I^}^{trig} ¦$ , introduced by Toledano Laredo, for an arbitrary root system $I^¦$ . We…

math.RT2025

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 $U g^{\otimes n}$ for arbitrary simple Lie algebra $g$ . This is the family of commutative subalgebras of ma…