Constructing G-algebras |
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Authors: | Kevin De Laet |
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Institution: | 1. Department of Mathematics, University of Antwerp, Antwerp, Belgiumkevin.delaet2@uantwerpen.be |
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Abstract: | In this article we define G-algebras, that is, graded algebras on which a reductive group G, acts as gradation preserving automorphisms. Starting from a finite dimensional G-module V and the polynomial ring ?V], it is shown how one constructs a sequence of projective varieties Vk such that each point of Vk corresponds to a graded algebra with the same decomposition up to degree k as a G-module. After some general theory, we apply this to the case that V is the n+1-dimensional permutation representation of Sn+1, the permutation group on n+1 letters. |
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Keywords: | Regular algebras representations of reductive groups |
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