2021/10/14 by Evgeny Feigin, Feigin, Evgeny, Igor Makhlin +3 · 1 citation
Mathematics · #Advanced Combinatorial Mathematics #Algebraic Geometry (math.AG) #Algebraic structures and combinatorial models #Combinatorics (math.CO) #Commutative Algebra and Its Applications #FOS: Mathematics #Representation Theory (math.RT)
paper · pdf · doi:10.48550/arxiv.2110.07397
openalex publication_date 2021/10/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study toric degenerations of semi-infinite Grassmannians (a.k.a. quantum\nGrassmannians). While the toric degenerations of the classical Grassmannians\nare well studied, the only known example in the semi-infinite case is due to\nSottile-Sturmfels. We start by providing a new interpretation of the\nSottile-Sturmfels construction by finding a poset such that their degeneration\nis the toric variety of the order polytope of the poset. We then use our poset\nto construct and study a new toric degeneration in the semi-infinite case. Our\nconstruction is based on the notion of poset polytopes introduced by\nFang-Fourier-Litza-Pegel. As an application we introduce semi-infinite\nPBW-semistandard tableaux, giving a basis in the homogeneous coordinate ring of\na semi-infinite Grassmannian.\n