2006 Fiscal Year Final Research Report Summary
A research on algebraic groups and Kac-Moody groups, and their applications
| Project/Area Number |
15540005
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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 | University of Tsukuba |
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Principal Investigator |
MORITA Jun University of Tsukuba, Graduate School of Pure and Applied Science, Professor, 大学院数理物質科学研究科, 教授 (20166416)
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| Project Period (FY) |
2003 – 2006
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| Keywords | algebraic groups / quantum group / integrability / tiling / extended affine Lie algebra / Kac conmiecture / combinatorics / conjugacy theorem |
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| Research Abstract |
(1) We introduced a new formulas for U q(sl_2), and gave a sufficient condition for its representation to be integrable.
(2) We gave a proof of the so-called Kac-conjecture for extended affine Lie algebras.
(3) We introduced certain bialgebras associated with given one-dimensional tilings, and gave a characterization for such tilings to be locally indistinguishable using our bialgebras.
(4) We constructed universal central extensions of certain adjoint groups associated with completed extended affine Lie algebras with nullity 2.
(5) We showed the fact that the groups and Lie algebras defined by one-dimensional tilings have standard and additive Gauss decompositions.
(6) We proved many conjugacy theorems for sl_2 of UFD algebras over fields, especially for Cartan subalgebras and for TDS as some analogue of Jacobson-Morozov theorem.
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