Geometric study of quantum groups and associative algebras

2015 Fiscal Year Final Research Report

• Project/Area Number: 24540008
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Algebra
• Research Institution: The University of Tokyo
• Principal Investigator: Saito Yoshihisa 東京大学, 数理(科)学研究科(研究院), 准教授 (20294522)
• Co-Investigator(Renkei-kenkyūsha): NAITO Satoshi 東京工業大学, 理工学研究科, 教授 (60252160) ; IYAMA Osamu 名古屋大学, 多元数理研究科, 教授 (70347532) ; TANISAKI Toshiyuki 大阪市立大学, 理学研究科, 教授 (70142916)
• Project Period (FY): 2012-04-01 – 2016-03-31
• Keywords: 結晶基底

Outline of Final Research Achievements

The main results of this research are the followings.
(1) Recently, Kamnitzer gave a new realization of crystal bases of the quantized enveloping algebras of finite types, by using the theory of Mirkovic-Vilinen polytopes which has originated in geometry of affine Grassmannian varieties. In this research, we constructed an analogue of these theories for affine quantized enveloping algebras.
(2) We studied characteristic varieties of intersection cohomology complexes of Schubert varieties in type A. More explicitly, by using the method of geometric realization of crystal cases, we determined the explicit forms of these varieties in low rank cases.

Free Research Field

表現論