1993 Fiscal Year Final Research Report Summary
Study of Prehomogeneous vector spaces
| Project/Area Number |
04640054
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| Research Category |
Grant-in-Aid for General Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Research Field |
代数学・幾何学
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| Research Institution | KYOTO UNIVERSITY |
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Principal Investigator |
GYOJA Akihiko Facutly of integrated Human studies, Kyoto University, Associate Professor, 総合人間学部, 助教授 (50116026)
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| Co-Investigator(Kenkyū-buntansha) |
NISHIYAMA Kyo Facutly of integrated Human studies, Kyoto University, Associate Professor, 総合人間学部, 助教授 (70183085)
YOSHINO Yuji Facutly of integrated Human studies, Kyoto University, Associate Professor, 総合人間学部, 助教授 (00135302)
MIYAMOTO Munemi Facutly of integrated Human studies, Kyoto University, Professor, 総合人間学部, 教授 (00026775)
KATO Sin-ichi Facutly of integrated Human studies, Kyoto University, Associate Professor, 総合人間学部, 助教授 (90114438)
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| Project Period (FY) |
1992 – 1993
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| Keywords | prehomogenous vector space / Lefschetz principle / Hecke algebra / R-matrix / automaton / Cohen-Macaulay module / Lie super algebra / irreducible unitary representation |
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| Research Abstract |
A.Gyoja improved the understanding of the Lefschetz principle in the theory of prehomogeneous vector spaces, using D-modules, mixed Hodge modules, perverse sheaves, etc. He also studied b-functions. Especially, he found an intimate relation between the b-functions of semi-invariants and the irreducibility of generalized Verma modules.
S.Kato showed that the duality of the representations of Hecke algebras can be obtained from an automorphism. He also constructed an R-matrix using Hecke algebras.
M.Miyamoto constructed stationary measures of automaton 90 and 150.
Y.Yoshino described the category of graded maximal Cohen-Macaulay modules, based on the Demazure representation of graded regular local rings. He also constructed a category of chain complexes which is equivalent to that of maximal Buchsbaum modules of finite projective dimension, and obtained a complete classification of such modules.
K.Nishiyama, with H.Furutsu, showed that all the irreducible unitary representation of the Lie superalgebra osp(m/n, R) can be realized using super dual pairs and the Weil representations.
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