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Let G be the split special orthogonal group of degree 2n+1 over a field F of charF≠2. Then we describe G-orbits on the triple flag varieties G/P×G/P×G/P and G/P×G/P×G/B with respect to the diagonal action of G where P is a maximal parabolic subgroup of G of the shape (n,1,n) and B is a Borel subgroup. As by-products, we also describe GLn-orbits on G/B, Q2n-orbits on the full flag variety of GL2n where...
Let p be an odd prime. We classify all self dual quadratic bent functions from Fpn to Fp under the action of the orthogonal group O(n,Fp). The sizes of the O(n,Fp)-orbits of such self dual bent functions are explicitly determined. These results are obtained through the following steps: 1. n×n symmetric matrices A over Fp satisfying A2=cI (c∈Fp⁎) are classified under the conjugation by O(n,Fp). 2....
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