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 , F 4 and G 2 over \(\mathbb{C}\), the projective variety \(\mathbb{P}(V^m)/W\) is projectively normal with respect to the descent of \(\mathcal{O}(1)^{\otimes |W|}\), where V m denote the direct sum of m copies of V.
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KANNAN, S., PATTANAYAK, S. Projective normality of Weyl group quotients. Proc Math Sci 121, 19–26 (2011). https://doi.org/10.1007/s12044-011-0007-x
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DOI: https://doi.org/10.1007/s12044-011-0007-x