On the Lagrangian Embedding of $${\rm U}(n)$$ in the Grassmannian $${\rm Gr} (n -1, 2 n -1)$$

In the present paper we combine our previous results in the studies of Lagrangian geometry of the Grassmannian $${\rm Gr} (k, n)$$ with the example of Lagrangian embedding of the full flag variety in the direct product of projective spaces, found by D. Bykov. As the result, we construct a Langrangian immersion of the group $${\rm U}(n)$$ , as a submanifold, into the complex Grassmanian $${\rm Gr} (n-1, 2 n-1)$$ equipped with the symplectic form, by the Plücker embedding. DOI 10.1134/S1061920824601770