2016 Fiscal Year Final Research Report
Study on the representation theory of affine Lie superalgebras and its applications
Project/Area Number |
24540014
|
Research Category |
Grant-in-Aid for Scientific Research (C)
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Allocation Type | Multi-year Fund |
Section | 一般 |
Research Field |
Algebra
|
Research Institution | University of Fukui |
Principal Investigator |
Koga Yoshiyuki 福井大学, 学術研究院工学系部門, 准教授 (20338429)
|
Project Period (FY) |
2012-04-01 – 2017-03-31
|
Keywords | 超リー代数 / ワイル亜群 |
Outline of Final Research Achievements |
In this research, we obtain the following results on highest weight representations over the affine Lie superalgebra of type sl(2,1): We study the structure of the Jantzen filtration of certain generalized Verma modules. As an application, we construct the BGG type resolutions of irreducible highest weight representations. Moreover, in order to describe the structure of generalized Verma modules by using the Weyl groupoid, we reveal a relation between the Weyl groupoids introduced by Heckenberger-Yamane and Sergeev-Veselov.
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Free Research Field |
表現論
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