On prehomogeneity of a rank variety
HTML articles powered by AMS MathViewer
- by Masaya Ouchi, Michio Hamada and Tatsuo Kimura PDF
- Proc. Amer. Math. Soc. 140 (2012), 4127-4129 Request permission
Abstract:
If a linear algebraic group $G$ acts on $M(m,n)$, then it also acts on a rank variety $M^{(r)}(m,n)=\{ X\in M(m,n)|\ \textrm {rank} X=r\}$. In this paper, we give the necessary and sufficient condition that this variety has a Zariski-dense $G$-orbit. We consider everything over the complex number field $\mathbb {C}.$References
- Tatsuo Kimura, Introduction to prehomogeneous vector spaces, Translations of Mathematical Monographs, vol. 215, American Mathematical Society, Providence, RI, 2003. Translated from the 1998 Japanese original by Makoto Nagura and Tsuyoshi Niitani and revised by the author. MR 1944442, DOI 10.1090/mmono/215
- Tatsuo Kimura, Shin-ichi Kasai, Masanobu Taguchi, and Masaaki Inuzuka, Some P.V.-equivalences and a classification of $2$-simple prehomogeneous vector spaces of type $\textrm {II}$, Trans. Amer. Math. Soc. 308 (1988), no.Β 2, 433β494. MR 951617, DOI 10.1090/S0002-9947-1988-0951617-6
- M. Sato and T. Kimura, A classification of irreducible prehomogeneous vector spaces and their relative invariants, Nagoya Math. J. 65 (1977), 1β155. MR 430336
Additional Information
- Masaya Ouchi
- Affiliation: Institute of Mathematics, University of Tsukuba, Ibaraki, 305-8571, Japan
- Email: msy2000@math.tsukuba.ac.jp
- Michio Hamada
- Affiliation: Institute of Mathematics, University of Tsukuba, Ibaraki, 305-8571, Japan
- Email: mhamada@math.tsukuba.ac.jp
- Tatsuo Kimura
- Affiliation: Institute of Mathematics, University of Tsukuba, Ibaraki, 305-8571, Japan
- Email: kimurata@math.tsukuba.ac.jp
- Received by editor(s): May 26, 2011
- Published electronically: April 13, 2012
- Communicated by: Lev Borisov
- © Copyright 2012
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 140 (2012), 4127-4129
- MSC (2010): Primary 11S90; Secondary 15A03
- DOI: https://doi.org/10.1090/S0002-9939-2012-11525-4
- MathSciNet review: 2957202