| Project/Area Number |
10640038
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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 | Josai University |
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Principal Investigator |
NAKAJIMA Haruhisa Josai University, Faculty of Science, Prof., 理学部, 教授 (90145657)
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| Co-Investigator(Kenkyū-buntansha) |
MIKI Hiroo Kyoto Institute of Technology, Faculty of Engineering, Prof., 工芸学部, 教授 (90107368)
YOSHIZAWA Mitsuo Josai University, Faculty of Science, Prof., 理学部, 教授 (40118774)
ISHIBASHI Hiroyuki Josai University, Faculty of Science, Prof., 理学部, 教授 (90118513)
SEKIGUCHI Katsusuke Kokushikan University, Faculty of Engineering, Asso.Prof, 工学部, 助教授 (20146749)
OGAWA Yoshito Tohoku Institute of Technology, Faculty of Engineering, Asso.Prof., 工学部, 助教授 (60160777)
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| Project Period (FY) |
1998 – 1999
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| Project Status |
Completed (Fiscal Year 1999)
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| Budget Amount *help |
¥3,300,000 (Direct Cost: ¥3,300,000)
Fiscal Year 1999: ¥1,300,000 (Direct Cost: ¥1,300,000)
Fiscal Year 1998: ¥2,000,000 (Direct Cost: ¥2,000,000)
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| Keywords | Classical Group / covariants / coregular / Swan group / relative equidimensionality / transvection / 有理式 / 共変式 / 相対的自明作用 |
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| Research Abstract |
A representation (V,G) of a reductive algebraic group G over the complex number field C is said to be coregular, if V//G is non-singular. For a semisimple G, irreducible coregular representations are determined by P.Littelemann, and for a simple G, all coregular representations are classified by V.L. Popov, G.W. Schwarz, O.M. Adomovich and E.O. Golovina. In this research, we have determined coregular representations of non-semisimple reductive groups G with simple semisimple parts having enouch closed orbits. This is based on the decomposition of actions of algebraic tori on normal varieties into no-blowing-up actions of codimension one and blowing-up actions of codimension 2. The Chow groups preserve under quotient morphisms in the latter actions. Moreover, in the relaion with this, we have studied relative equidimensionalities and relative stabilities of actions of non-semisimple reductive groups and obtain some results which are useful in classifying coregular or equidimensional rep
… More
resentaions.
We generalize a part of the classical ramification theory of finite Galois groups to one of quotient morphisms under affine group actions and give a criterion the result similar to in finite covering cases to hold in affine groups case, which is related to an extension of some results on semi-invariants of finite groups to in the case of centric diconnected tori.
In order to study on invariant theory of classical groups over local rings, we give a nice criterion for a set of symplectic trasvections to be a genrating system of the sympectic group Sp(V) defined over local rings (due to Ishibashi).
On representaion theory of finite groups: We determine essential ideals and primary decompositions of mod 2-cohomology ring of finite abelian 2-groups (due to Ogawa) and obtain partial results on extensions of some 2-groups which preserve the irresucibilities of induced characters (due to Sekiguchi). These results seem to be useful in studying functor properties in invariant theory of finite groups. Less
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