A proof of the Popov conjecture for tori
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- by David L. Wehlau PDF
- Proc. Amer. Math. Soc. 114 (1992), 839-845 Request permission
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).References
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Additional Information
- © Copyright 1992 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 114 (1992), 839-845
- MSC: Primary 14L30; Secondary 20G45
- DOI: https://doi.org/10.1090/S0002-9939-1992-1074757-9
- MathSciNet review: 1074757