Gelfand–Tsetlin varieties for 𝔤𝔩n

Abstract

Sergei Ovsienko proved that the Gelfand–Tsetlin variety for [Formula: see text] is equidimensional and the dimension of all irreducible components equals [Formula: see text]. This implies in particular the equidimensionality of the nilfiber of the (partial) Kostant–Wallach map. We generalize this result for the [Formula: see text]-partial Kostant–Wallach map and prove that all its fibers are equidimensional of dimension [Formula: see text]. Also, we study certain subvarieties of the Gelfand–Tsetlin variety and show their equidimensionality which gives a new proof of Ovsienko’s theorem for [Formula: see text] and [Formula: see text].