2013 Fiscal Year Final Research Report
On representation theory from the view point of integrable systems
| Project/Area Number |
22540048
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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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 | Okayama University |
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Principal Investigator |
SUZUKI Takeshi 岡山大学, 自然科学研究科, 准教授 (30335294)
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| Project Period (FY) |
2010-04-01 – 2014-03-31
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| Keywords | Cherednik代数 / Hecke代数 / Lie代数 / 共形場理論 / 圏化 / 表現論 / 量子群 |
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| Research Abstract |
We studied on the graded Cartan matrices for the Khovanov-Lauda-Rouquier algebras associated to the Iwahori-Hecke algebras of type A. As a result, we obtained several explixit and combinatorial descriptions for their determinants, and conjectual expressions for their elementary divisors.
We also studied on representations for the Cherednik algebra of type GL_n. We focused on irreducible representations which are described in terms of cylindric standard tableaux. By applying cylindric combinatorics, we investigated their structure and their relation to the representatinos of the affine Lie algebra via conformal field theory.
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Research Products
(9 results)
