2010 Fiscal Year Final Research Report
Moduli of representations and related topics
| Project/Area Number |
19740007
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Single-year Grants |
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| Research Field |
Algebra
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| Research Institution | University of Yamanashi |
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Principal Investigator |
NAKAMOTO Kazunori University of Yamanashi, 総合分析実験センター, 教授 (30342570)
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| Project Period (FY) |
2007 – 2010
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| Keywords | 代数学 / 代数幾何学 / 不変式論 / 表現のモジュライ |
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| Research Abstract |
We described rational homotopy types and mixed Hodge structuresof the moduli of representations with Borel mold over the complex number field for the free algebras. We also investigated topological structures of the representation varieties with Borel mold. In other words, we described topological structures of the moduli of representations explicitly for fundamental cases. We studied a certain class of irreducible representations that is called "thick". We described the moduli of 4-dimensional non-thick irreducible representations for the free group of rank 2. Furthermore, we obtained the degenerated Poincare series of degree 6 for determining the structure of the matrix invariant ring.
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