Projective normality of Weyl group quotients

2010/07/05 by S. Senthamarai Kannan, S. S. Kannan, Kannan, S. S. +3
Mathematics · #14 Algebraic Geometry #Advanced Algebra and Geometry #Advanced Combinatorial Mathematics #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Representation Theory (math.RT) #math.AG #math.RT #msc:14

paper · pdf · doi:10.48550/arxiv.1007.0606

10 pages

openalex publication_date 2010/07/05 · arxiv created 2010/07/08 · arxiv updated 2010/07/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this note, we prove that for the standard representation Vof the Weyl group W of a semi-simple algebraic group of type A_n, B_n, C_n, D_n, F₄ and G₂ over \mathbb C, the projective variety \mathbb P(V^m)/W is projectively normal with respect to the descent of \mathcal O(1)^{⊗ |W|}, where V^m denote the direct sum of m copies of V. We also prove that for any finite group G and for any finite dimentional representation V over \mathbb C, the projective variety P(V)/G is projectively normal with respect to the descent of \mathcal O(1)^{⊗ n!} as a consequence.

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