A structure theorem for prehomogeneous vector spaces


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	A structure theorem for prehomogeneous vector spaces


	Fixed Point Theory, Volume 20, No. 1, 2019, 271-288, February 1st, 2019 DOI: 10.24193/fpt-ro.2019.1.18 Authors: Masaya Ouchi Abstract: In this note, we give a structure theorem for all prehomogeneous vector spaces defined over the complex number field C. Also it means a necessary and sufficient condition for a triplet (G, ρ, V) defined over C to be a prehomogeneous vector space. For this purpose, we give a general structural correspondence between isotropy subgroups and fixed point sets when a group acts on a non-empty set. Key Words and Phrases: Prehomogeneous vector space, representation theory of groups, fixed point. 2010 Mathematics Subject Classification: 11S90, 20Cxx. Published on-line: February 1st, 2019. Abstract pdf Fulltext pdf Back to volume's table of contents