Relative invariants of some 2-simple prehomogeneous vector spaces

Authors:
Takeyoshi Kogiso, Go Miyabe, Miyuki Kobayashi and Tatsuo Kimura

Journal:
Math. Comp. **72** (2003), 865-889

MSC (2000):
Primary 11S05, 11S90

DOI:
https://doi.org/10.1090/S0025-5718-02-01470-9

Published electronically:
October 18, 2002

MathSciNet review:
1954972

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Abstract | References | Similar Articles | Additional Information

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.

**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:
https://doi.org/10.1090/S0025-5718-02-01470-9

Received by editor(s):
April 20, 2000

Received by editor(s) in revised form:
May 29, 2001

Published electronically:
October 18, 2002

Article copyright:
© Copyright 2002
American Mathematical Society