manuscripta mathematica

, Volume 102, Issue 2, pp 139–158 | Cite as

Relative equidimensionality and stability of actions¶of a reductive algebraic group

  • Haruhisa Nakajima


In order to inquire into invariants of non-semisimple groups, we introduce and study relative versions of equidimensionality and stabilty, which are called relative quasi-equidimensionality and relative stability, of actions of affine algebraic groups, especially of reductive groups, on affine varieties. As an application of our results, for complex reductive groups of semisimple rank one, we characterize, respectively, relatively stable representations and relatively equidimensional representations and, consequently, show that every equidimensional representation is cofree.

Mathematics Subject Classification (1991):20G05, 14L30, 14L24, 13A50 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2000

Authors and Affiliations

  • Haruhisa Nakajima
    • 1
  1. 1.Department of Mathematics, Faculty of Science, Josai University, Keyakidai 1-1, Sakado 350-0295, JapanJP

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