中科院数学与系统科学研究院

数学研究所

中科院华罗庚数学重点实验室

综合报告会

（Colloquium）

报告人：ARIKI, susumu (有木進)(Osaka University)

题  目：Lifting Schur positive polynomials to Kashiwara crystals

时  间：2018.12.20(星期四) , 16:30-17:30(16:00-16:30为茶点时间, 地点: 数学院南楼N920室)

地  点：数学院南楼N913室

注：该讲座茶点受到中链科技有限公司的资助

摘 要：

Masaki Kashiwara, a recipient of Kyoto prize and Chern medal this year, invented Kashiwara crystal in early 1990’s. In type A, highest weight crystals give Schur polynomials as their characters. A Schur positive polynomial is a symmetric polynomial with integral coefficients which admits expression as (positive) sum of Schur polynomials. For a Schur positive polynomial, we may expect that there exists a crystal whose character is the given polynomial such that an isomorphism of crystals explains the identity that it is equal to sum of Schur polynomials. We give several examples of this kind. They include those using ghost leg or grid class.