论文标题
苏唑晶体的多面体参数化的舒伯特演算
Schubert calculus from polyhedral parametrizations of Demazure crystals
论文作者
论文摘要
舒伯特微积分的一种方法是将舒伯特类作为混凝土组合对象，例如舒伯特多项式。通过鉴定A型A型的共同体环，具有Gelfand-Tsetlin多面体的多型环，Kiritchenko-Smirnov-Timorin将每个Schubert class都视为减少（双重）Kogan脸的总和。在本文中，我们明确地描述了相反的氮杂晶体的弦参数化，从而使减少的双重kogan脸具有自然的概括。我们还使用有丝分裂算子的理论将减少的Kogan面孔与项晶体联系起来，并应用这些观察结果将Schubert Colculus的理论发展在符号Gelfand-Tsetlin多面体上。
One approach to Schubert calculus is to realize Schubert classes as concrete combinatorial objects such as Schubert polynomials. Through an identification of the cohomology ring of the type A full flag variety with the polytope ring of the Gelfand-Tsetlin polytopes, Kiritchenko-Smirnov-Timorin realized each Schubert class as a sum of reduced (dual) Kogan faces. In this paper, we explicitly describe string parametrizations of opposite Demazure crystals, which give a natural generalization of reduced dual Kogan faces. We also relate reduced Kogan faces with Demazure crystals using the theory of mitosis operators, and apply these observations to develop the theory of Schubert calculus on symplectic Gelfand-Tsetlin polytopes.
