Remote Access Mathematics of Computation
Green Open Access

Mathematics of Computation

ISSN 1088-6842(online) ISSN 0025-5718(print)

 
 

 

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
Full-text PDF

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.


References [Enhancements On Off] (What's this?)

  • 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.

Similar Articles

Retrieve articles in Mathematics of Computation with MSC (2000): 11S05, 11S90

Retrieve articles in all journals with MSC (2000): 11S05, 11S90


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

American Mathematical Society