We study the PBW filtration on the highest weight representations V (λ) of sl _ n+ 1. This
filtration is induced by the standard degree filtration on U\left (n^-\right). We give a …

Combinatorial reciprocity is a very interesting phenomenon, which can be described as
follows: A polynomial, whose values at positive integers count combinatorial objects of some …

We study the PBW filtration on the highest weight representations V (λ) of sp_2n. This
filtration is induced by the standard degree filtration on U(n^-). We give a description of the …

Following the historical track in pursuing T-equivariant flat toric degenerations of flag
varieties and spherical varieties, we explain how powerful tools in algebraic geometry and …

We introduce the notion of a favourable module for a complex unipotent algebraic group,
whose properties are governed by the combinatorics of an associated polytope. We …

We determine the number of complex solutions to a nonlinear eigenvalue problem on the
Grassmannian in its Plücker embedding. This is motivated by quantum chemistry, where it …

We introduce in this paper the marked chain-order polytopes associated to a marked poset,
generalizing the marked chain polytopes and marked order polytopes by putting them as …

Gelfand--Tsetlin polytopes are prominent objects in algebraic combinatorics. The number of
integer points of the Gelfand--Tsetlin polytope GT(λ) is equal to the dimension of the …

The two best studied toric degenerations of the flag variety are those given by the Gelfand–
Tsetlin and FFLV polytopes. Each of them degenerates further into a particular monomial …

We study the closure of the graph of the birational map from a projective space to a
Grassmannian. We provide explicit description of the graph closure and compute the fibers …