Quantized Schur algebras, Koszul duality and categorifications

2016 Fiscal Year Final Research Report

• Project/Area Number: 24740011
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Multi-year Fund
• Research Field: Algebra
• Research Institution: Osaka City University
• Principal Investigator: MIYACHI Hyohe 大阪市立大学, 大学院理学研究科, 准教授 (90362227)
• Research Collaborator: Chlouveraki Maria ; Chuang Joseph ; Fang Ming ; Leclerc Bernard ; Rouquier Raphael ; Tan Kai Meng ; KUWABARA Toshiro
• Project Period (FY): 2012-04-01 – 2017-03-31
• Keywords: 表現論 / 量子群 / Hecke環 / 準遺伝的多元環 / 圏化 / 導来同値

Outline of Final Research Achievements

About 100 years ago, Representation Theory launched. There are various mathematical research fields such as algebras, geometry and analysis, and Representation Theory interacts with them. One of the most important thing in High school chemistry is the notion of atom, which represents the smallest basic unit. In Representation Theory, the corresponding notion is the simple object. Moreover, molecules in High school chemistry are also important. In a sense, the corresponding notion of these in Representation Theory are projective indecomposable objects, which are extended as unbreakable units by simple objects as possible.
By standing on the shoulder of giants, we knew that those two kinds of objects are interpreted as two kinds of Lusztig's canonical bases also known as Kashiwara's global crystal bases in the research area on this report. Based on those interpretation we found in the category theory a natural interpretation on exchanging those two kinds of objects.

Free Research Field

表現論