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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

A proof of the Popov conjecture for tori


Author: David L. Wehlau
Journal: Proc. Amer. Math. Soc. 114 (1992), 839-845
MSC: Primary 14L30; Secondary 20G45
MathSciNet review: 1074757
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Abstract: We prove a lemma which reduces much of the invariant theory of torus representations to the theory of faithful stable torus representations (Lemma 2). Using this reduction we obtain a structure theorem (Theorem 1) for equidimensional representations of tori. This theorem shows that the weights of an equidimensional torus representation are arranged in a very special manner within the lattice of characters. Understanding this arrangement allows us to prove that equidimensional representations of tori must be cofree (the Popov conjecture for tori).


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DOI: http://dx.doi.org/10.1090/S0002-9939-1992-1074757-9
PII: S 0002-9939(1992)1074757-9
Article copyright: © Copyright 1992 American Mathematical Society