K-theoretic Schubert Calculus for Grassmannians

2020 Fiscal Year Final Research Report

• Project/Area Number: 16K17584
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Multi-year Fund
• Research Field: Algebra
• Research Institution: International Christian University (2020); Okayama University of Science (2016-2019)
• Principal Investigator: Matsumura Tomoo 国際基督教大学, 教養学部, 准教授 (80755223)
• Project Period (FY): 2016-04-01 – 2021-03-31
• Keywords: シューベルト多項式 / シュアー多項式 / グロタンディック多項式 / 旗多様体 / グラスマン多様体

Outline of Final Research Achievements

The main result obtained from this research was the K-theoretic extensions of the proof of the determinant formula of type A Grassmannian Schubert classes by Kempf-Laksov and Damon and the Pfaffian formula of type C Lagrangian Grassmannian Schubert classes by Kazarian. As a consequence, we understand algebraic and combinatorial aspects of the Grothendieck polynomials. Based on this result, we will work on determining the Schubert coefficients for type C Grassmannians in future work.

Free Research Field

代数・組み合わせ論・幾何学

Academic Significance and Societal Importance of the Research Achievements

C型のシューベルトカルキュラスに関しては、シューベルト係数を求めるという問題は未解決の部分が多い。そんな中、シューベルト類の良い表示を代数的にも組み合わせ論的にも得られたことは、大きな進展であったと考える。