Our main goal is to show that the Gelfand–Tsetlin toric degeneration of the type A ag variety can be obtained within a degenerate representation-theoretic framework similar to the theory of PBW degenerations. In fact, we provide such frameworks for all Gröbner degenerations intermediate between the ag variety and the GT toric variety. These degenerations are shown to induce filtrations on the irreducible representations and the associated graded spaces are acted upon by a certain associative algebra. To achieve our goal, we construct embeddings of our Gröbner degenerations into the projectivizations of said associated graded spaces in terms of this action. We also obtain an explicit description of the maximal cone in the tropical ag variety that parametrizes the Gröbner degenerations we consider. In an addendum we propose an alternative solution to the problem which relies on filtrations and gradings by non-abelian ordered semigroups.

我们的主要目标是证明可以在类似于PBW退化理论的退化表征理论框架中获得A型ag变种的Gelfand-Tsetlin复曲面。实际上，我们为介于Ag品种和GT Toric品种之间的所有Gröbner变性提供了此类框架。这些退化被显示为在不可约表示上引起过滤，并且相关的分级空间受到某个关联代数的作用。为了实现我们的目标，就此操作而言，我们将Gröbner变性的嵌入项构造到所述相关渐变空间的投影化中。我们还获得了对热带ag品种中最大锥的明确描述，该参数使我们考虑的Gröbner变性参数化。