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Relative invariants of some 2-simple prehomogeneous vector spaces
Author(s):
Takeyoshi
Kogiso;
Go
Miyabe;
Miyuki
Kobayashi;
Tatsuo
Kimura.
Journal:
Math. Comp.
72
(2003),
865-889.
MSC (2000):
Primary 11S05, 11S90
Posted:
October 18, 2002
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Abstract:
In this paper, we shall construct explicitly irreducible relative invariants of two 2-simple prehomogeneous vector spaces. Together with a preprint by the same authors, this completes the list of all relative invariants of regular 2-simple prehomogeneous vector spaces of type I.
References:
-
- 1.
- M. Sato and T. Kimura , A classification of irreducible prehomogeneous vector spaces and their relative invariants, Nagoya Math. J., 65, (1977), 1-155. MR 55:3341
- 2.
- T. Kimura, A classification of prehomogeneous vector spaces of simple algebraic groups with scalar multiplications, J. Algebra, 83, No. 1, (1983), 72-100. MR 85d:32059
- 3.
- T. Kimura, Remark on some combinatrial construction of relative invariants, Tsukuba J. Math. 5, (1981), 101-115. MR 84g:20078
- 4.
- J. Igusa, A classification on spinors up to dimension twelve, Amer. J. Math. 92, (1970), 997-1028. MR 43:3291
- 5.
- J. Igusa, On arithmetic of a singular invariant, Amer. J. Math. 110, (1988), 197-233. MR 86g:11116
- 6.
- H. Kawahara, Prehomogeneous vector spaces related with the spin group, Master Thesis, University of Tokyo, (1974) (Japanese).
- 7.
- A. Gyoja, Construction of invariants, Tsukuba J. Math. 14, (1990), No. 2, 437-457. MR 91k:22035
- 8.
- H. Ochiai, Quotients of some prehomogeneous vector spaces, J. Algebra, 192, (1997), No. 1, 61-73. MR 98g:14059
- 9.
- T. Kimura, S. Kasai, M. Inuzuka and O. Yasukura, A classification of 2-simple prehomogeneous vector spaces of type I, J. Algebra, 114, No. 2, (1988), 369-400. MR 89f:32062
- 10.
- T. Kogiso, G. Miyabe, M. Kobayashi and T. Kimura, Explicit construction of relative invariants for regular 2-simple prehomogeneous vector spaces of type I, preprint
- 11.
- T. Kogiso, G. Miyabe, M. Kobayashi and T. Kimura, Nonregular 2-simple prehomogeneous vector spaces of type I and their relative invariants, J. Algebra, 251, 27-69 (2002).
- 12.
- Mathematica, Wolfram Research Inc.
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Additional Information:
Takeyoshi
Kogiso
Affiliation:
The Department of Mathematics, Josai University, Saitama, 305-0295, Japan
Email:
kogiso@math.josai.ac.jp
Go
Miyabe
Affiliation:
The Institute of Mathematics, University of Tsukuba, Ibaraki, 305-8571, Japan
Email:
subaru@first.tsukuba.ac.jp
Miyuki
Kobayashi
Affiliation:
The Institute of Mathematics, University of Tsukuba, Ibaraki, 305-8571, Japan
Email:
miyuki@math.tsukuba.ac.jp
Tatsuo
Kimura
Affiliation:
The Institute of Mathematics, University of Tsukuba, Ibaraki, 305-8571, Japan
Email:
kimurata@math.tsukuba.ac.jp
DOI:
10.1090/S0025-5718-02-01470-9
PII:
S 0025-5718(02)01470-9
Received by editor(s):
April 20, 2000
Received by editor(s) in revised form:
May 29, 2001
Posted:
October 18, 2002
Copyright of article:
Copyright
2002,
American Mathematical Society
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