Study of mod p representations of p-adic groups

2017 Fiscal Year Final Research Report

• Project/Area Number: 26707001
• Research Category: Grant-in-Aid for Young Scientists (A)
• Allocation Type: Partial Multi-year Fund
• Research Field: Algebra
• Research Institution: Hokkaido University
• Principal Investigator: Abe Noriyuki 北海道大学, 理学研究院, 准教授 (00553629)
• Project Period (FY): 2014-04-01 – 2018-03-31
• Keywords: 既約表現 / p進群 / 法p表現

Outline of Final Research Achievements

Langlands conjecture is a conjecture which includes, for example, Femrat's conjecture. Representation theory of p-adic groups is a part of this conjecture. I studied modulo p representations of p-adic groups. I proved a classification theorem of such representations (with collaborators) and the images of certain functors of these representations are calculated. I also studied pro-p-Iwahori Hecke algebra which plays an important role in the proof of the classification theorem. I classified simple modules, calculated extensions between simple modules and studied the relations between modulo p representations.

Free Research Field

表現論