1998 Fiscal Year Final Research Report Summary
Represontation theory of algebraic groups
| Project/Area Number |
09440018
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| Research Category |
Grant-in-Aid for Scientific Research (B)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Algebra
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| Research Institution | HIROSHIMA UNIVERSITY |
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Principal Investigator |
TANISAKI Toshiyuki Faculty of Science, HIROSHIMA UNIVERSITY Professor, 理学部, 教授 (70142916)
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| Co-Investigator(Kenkyū-buntansha) |
KANEDA Masaharu Osaka City University, Faculty of Science Professor, 理学部, 教授 (60204575)
KASHIWARA Nasaki Kyoto University, Research Instute for Mathomatical Sciences Professor, 数理解析研究所, 教授 (60027381)
MORITA Yashiyuki Faculty of Science Assistant, 理学部, 助手 (20243545)
KANNO Hiroaki Faculty of Science Assistant Professor, 理学部, 助教授 (90211870)
SUMIHIRO Hideyasu Faculty of Science Professor, 理学部, 教授 (60068129)
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| Project Period (FY) |
1997 – 1998
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| Keywords | algebraic groups / Lie algebras / Quantum groups |
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| Research Abstract |
1. Highest weight modules over affine Lie algebras
The head organizer and Masaki Kashiwara investigated on characters of irreducible highest weight modules over affine Lie algebras. We first proved Kazhdan-Lusztig type character formula for the irreducible modules with rational non-critical highest weights, and next generalized it to arbitrary non-critical weights. One of the next problems is to determine characters of the irreducible modules with critical highest weights and to investigate its geometyric back ground.
2. Generalized hypergeometric systems and Radon-Penrose transforms.
The head organizer investigated on Radon-Penrose transforms between flag manifolds using the theory of weakly equivariant D-modules, and gave sufficient conditions in order that it is injective or surjective in the sence of the D-module theory. Moreover, I studied the condition in each indivisual cases. One of the next problems is to determin the image and the kernel of the Radon transform.
3. Quantum deformations of prehomogeneous vector spaces
The head organizer and Yoshiyuki Morita constructed quantum deformations for the coordinate algebras of the prehomogenous vector spaces of parabolic type. Morita further applied this result to exceptional simple Lie algebras, and gave an explicit description of the quantume deformation of the exceptional prehomogeneous vector spaces and its relative invariants.
One of the next problems are to investigate of the quantum counter part of the theory of prehomogeneous vector spaces related to number theoretic direction such as zeta functions.
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