Modular representations of algebraic groups

2014 Fiscal Year Final Research Report

• Project/Area Number: 23540023
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Algebra
• Research Institution: Osaka City University
• Principal Investigator: KANEDA masaharu 大阪市立大学, 大学院・理学研究科, 教授 (60204575)
• Co-Investigator(Renkei-kenkyūsha): TANISAKI Toshiyuki 大阪市立大学, 大学院理学研究科, 教授 (70142916) ; YAGITA Nobuaki 茨城大学, 教育学部, 教授 (20130768) ; TEZUKA Michishige 琉球大学, 理学部, 教授 (20197784) ; FURUSAWA Masaaki 大阪市立大学, 大学院理学研究科, 教授 (50294525) ; HASHIMOTO Yoshitake 東京都市大学, 知識工学部, 教授 (20271182) ; KAWATA Shigeto 大阪市立大学, 大学院理学研究科, 准教授 (50195103)
• Project Period (FY): 2011-04-28 – 2015-03-31
• Keywords: 代数群 / modular表現 / Frobenius kernel / 量子群 / flag variety / cohomology

Outline of Final Research Achievements

Let G be a reductive algebraic group over an algebraically closed field of positive characteristic p, P a parabolic subgroup of G, and T a maximal torus of P,
G_1 the Frobenius kernel of G. In joint work with Abe Noriyuki we determined the G_1T-structure of G_1P-Verma modules of p-regular highest weights for large p.
In joint work with H.H. Andersen we determined the cohomology vanishing behavior of line bundles on G/B in type G_2 when the corresponding B-modules lie in the lowest p^2-alcoves. In join work with M. Gros we constructed a Frobenius splitting on a quantum group at a root of unity.

Free Research Field

群論