$({\mathfrak{gl}}_n,{\mathfrak{gl}}_m)$-duality and Olshanski homomorphism

B. Feigin, L. Rybnikov, F. Uvarov

We show that the images of the Bethe subalgebras of the Yangians $Y({\mathfrak{gl}}_n)$ and $Y({\mathfrak{gl}}_m)$ under the homomorphisms to $U({\mathfrak{gl}}_{n+m})$ given by the…