On the Clifford Collineation, Transform and Similarity Groups (IV): An Application to Quadratic Forms

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Abstract
E. S. Barnes and I recently constructed a series of positive quadratic forms fN in N = 2n variables (n = 1, 2,…) with relative minima of order for large N. I continue this investigation by determining the minimal vectors of fN and showing that, for its group of automorphs is the Clifford group This suggests a generalization. Replacing by where p is an odd prime, I derive a new series of positive forms in N =(p−1)pn variables (§4). The relative minima are again of order (p fixed, N → ∞ ), the “best” forms being those for p = 3, 5. All forms are eutactic though only those for p = 3,5 are extreme.

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