Research on generalized cohomology of flag varieties and Schur functions and their variants

2017 Fiscal Year Final Research Report

• Project/Area Number: 15K04876
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Geometry
• Research Institution: Okayama University
• Principal Investigator: Nakagawa Masaki 岡山大学, 教育学研究科, 准教授 (50370036)
• Co-Investigator(Kenkyū-buntansha): 成瀬 弘 山梨大学, 大学院総合研究部, 教授 (20172596)
• Co-Investigator(Renkei-kenkyūsha): IKEDA Takeshi 岡山理科大学, 理学部, 教授 (40309539) ; NAKADA Kento 岡山大学, 教育学研究科, 准教授 (70532555)
• Project Period (FY): 2015-04-01 – 2018-03-31
• Keywords: トポロジー / 旗多様体 / 一般コホモロジー / Schur関数 / Hall-Littlewood関数 / Gysin写像 / 複素コボルディズム / シューベルト・カルキュラス

Outline of Final Research Achievements

We studied a generalization of the Gysin formulas for the Hall-Littlewood polynomials due to Pragacz to the complex-oriented generalized cohomology theory. We introduced the universal Hall-Littlewood functions, and established the universal Gysin formulas for them. We also studied a generalization of the Darondeau-Pragacz formulas in the ordinary cohomology theory to the complex cobordism theory, and extended their formulas in the case of type A flag bundles. In the course of our study, we introduced the universal factorial Hall-Littlewood P- and Q-functions, and were able to obtain the generating functions for them as a by-product of our formulas.

Free Research Field

数学, 幾何学, トポロジー