2023/06/26 by Fujita, Naoki, Nishiyama, Yuta
#14N15 #Algebraic Geometry (math.AG) #Combinatorics (math.CO) #FOS: Mathematics #Primary 05E10 #Representation Theory (math.RT) #Secondary 14M15
paper · doi:10.48550/arxiv.2306.14485
An approach to Schubert calculus is to realize Schubert classes as concrete combinatorial objects such as Schubert polynomials. Using the polytope ring of the Gelfand-Tsetlin polytopes, Kiritchenko-Smirnov-Timorin realized each Schubert class as a sum of reduced Kogan faces. The first named author introduced a generalization of reduced Kogan faces to symplectic Gelfand-Tsetlin polytopes using a semi-toric degeneration of a Schubert variety, and extended the result of Kiritchenko-Smirnov-Timorin to type C case. In this paper, we introduce a combinatorial model to this type C generalization using a kind of pipe dream with self-crossings. As an application, we prove that the type C generalization can be constructed by skew mitosis operators.