| Project/Area Number |
17340012
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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 | Osaka City University |
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Principal Investigator |
TANISAKI Toshiyuki Osaka City University, Graduate School of science, professor, 大学院理学研究科, 教授 (70142916)
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| Co-Investigator(Kenkyū-buntansha) |
KASHIWARA Msaki Kyoto Univ., RIMS, professor, 数理解析研究所, 教授 (60027381)
SHOJI Toshiaki Nagoya Univ., Graduate school of Mathematics, professor, 多元数理科学研究科, 教授 (40120191)
SAITO Yoshihisa Univ.Tokyo, Graduate school of Mathemtaical sciences, assistant professor, 数理科学研究科, 助教授 (20294522)
KANEDA Msaharu Osaka City University, Graduate school of science, professor, 大学院理学研究科, 教授 (60204575)
NAKAJIMA Hiraku Kyoto Univ., Graduate school of science, professor, 理学研究科, 教授 (00201666)
竹内 潔 筑波大学, 大学院数理物質科学研究科, 助教授 (70281160)
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| Project Period (FY) |
2005 – 2006
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| Project Status |
Completed (Fiscal Year 2006)
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| Budget Amount *help |
¥9,100,000 (Direct Cost: ¥9,100,000)
Fiscal Year 2006: ¥5,300,000 (Direct Cost: ¥5,300,000)
Fiscal Year 2005: ¥3,800,000 (Direct Cost: ¥3,800,000)
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| Keywords | Lie algebras / Quantum groups / Algebraic analysis |
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| Research Abstract |
1. Tanisaki investigated the action of the braid groups on the zero-weight spaces of the integral modules over quantized enveloping algebras. Under a certain condition on the representation the braid group action descends to the Hecke algebra, and a module over the Hecke algebra is obtained. In the case of type A all irreducible modules over the Hecke algebra is derived. Using the Kazhdan-Lusztig bases for the Hecke algebra modules and the global bases for the modules over the quantized enveloping algebras we can show that the construction above makes sense over rings. Hence it is possible to investigate modular representations by this method. Tanisaki gave a new proof of the conjecture by Lascoux-Leclerc-Thibon.
2. Tanisaki investigated applications of the geometric Langlands correspondence to representation theory. Especially, he tried to obtain the twining character formula due to Naito etc. using geometric Langalands correspondence.
3. Kashiwra investigated level zero fundamental modules over affine quantum algebras and Demazure modules.
4. Shoji investigated representations of modified Ariki-Koike algebras introduced by himself. He also obtained interesting results on the corresponding q-Shur algebras.
5. Naito investigated crystal bases of the extremal weight modules. Especially, he considered about the action of the diagram automorphisms and obtained results about the elements of the crystal base fixed by this group.
6. Satio investigated Macdonald polynomials using Cherednik algebras.
7. Kashiwara investigated representations of affine Hecke algebras of type B.
8. Shoji investigated generalized Green functions and obtained results about some constant.
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