2024/03/15 by Ievgen Makedonskyi, Makedonskyi, Ievgen, Igor Makhlin +1
Computer Science · Mathematics · #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Algebraic Geometry (math.AG) #Combinatorics (math.CO) #FOS: Mathematics #Representation Theory (math.RT) #semigroups and automata theory
paper · pdf · doi:10.48550/arxiv.2403.09959
openalex publication_date 2024/03/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We demonstrate how pipe dreams can be applied to the theory of poset polytopes to produce toric degenerations of flag varieties. Specifically, we present such constructions for marked chain-order polytopes of Dynkin types A and C. These toric degenerations also give rise to further algebraic and geometric objects such as PBW-monomial bases and Newton--Okounkov bodies. We discuss a construction of the former in the type A case and of the latter in type C.