Research on the loop spaces on Lie groups by combinatorial methods

2014 Fiscal Year Final Research Report

• Project/Area Number: 24540105
• 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(研究院), 准教授 (50370036)
• Co-Investigator(Renkei-kenkyūsha): TAKESHI Ikeda 岡山理科大学, 理学部, 教授 (40309539) ; NARUSE Hirhoshi 山梨大学, 大学院総合研究部, 教授 (20172596)
• Project Period (FY): 2012-04-01 – 2015-03-31
• Keywords: トポロジー / 幾何学 / リー群 / ループ空間 / 組合せ論 / 一般コホモロジー理論

Outline of Final Research Achievements

(1)Using the universal formal group law in complex cobordism theory, we introduced a new family of symmetric functions, which is a generalization of the usual factorial Schur P- and Q-functions due to Ivanov. Using these symmetric functions, we gave a description of the complex oriented generalized (co)homology Hopf algebras of the loop spaces on the infinite symplectic and special orthogonal group. Furthermore, we showed the various properties of these functions such as factorization property, vanishing property, and basis theorem.
(2)We also introduced a generalization of the usual factorial Schur functions. We gave a characterization of these symmetric functions via the Gysin homomorphism for the flag bundle associated with a complex vector bundle in complex oriented generalized cohomology theory.

Free Research Field

数物系科学