Partial orthogonal spreads over $\mathbb{F}_2$ invariant under the symmetric and alternating groups

12 Aug 2016 Gow Rod

Let m be an integer greater than 2 and let V be a vector space of dimension 2^m over F_2. Let Q be a non-degenerate quadratic form of maximal Witt index defined on V. We show that the symmetric group S_{2m+1} acts on V as a group of isometries of Q and permutes the members of a partial orthogonal spread of size 2m+1... (read more)

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Categories


  • GROUP THEORY
  • REPRESENTATION THEORY